Seminars - Historic

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Disproving the Deift conjecture: the loss of almost periodicity
Speaker: Andreia Chapouto (University of Edinburgh, UK)
The Korteweg-de Vries equation (KdV), derived in the late 1800's to describe shallow-water waves, is one of the simplest but most fundamental examples of a partial differential equation combining nonlinear and dispersive effects. In constructing solutions, we often assume that particular...

Density of group languages in shift spaces
Speaker: Herman Goulet-Ouellet (Czech Technical University, Prague)
I will present some ongoing work about densities of regular languages in minimal shift spaces. We will focus on the density of group languages, i.e. languages recognized by morphisms onto finite groups. Working within the skew product of the shift space and the recognizing group, a simple...

On chain polynomials of posets
Speaker: Leonardo Saud Maia Leite (KTH Royal Institute of Technology, Sweden)
The chain polynomial of a finite lattice \( \mathcal{L} \) is given by \( p_\mathcal{L} (x) = \sum_{k \geq 0} c_k(\mathcal{L})x^k \), where \( c_k(\mathcal{L}) \) is the number of chains of length \( k \) in \( \mathcal{L} \). The chain polynomials of posets in several important classes have...

Divided difference (quantum) operators: from Fourier expansions to function spaces associated with their inverse
Speaker: José Luis Cardoso (UTAD)

Demazure keys, virtual keys and Schubert varieties
Speaker: Olga Azenhas (CMUC, Univ. Coimbra)
Demazure modules, opposite and their intersection are in natural correspondence respectively with Schubert varieties, opposite and  Richardson varieties. The classical Borel-Weil theorem explains this correspondence. It provides a geometric definition of irreducible highest weight...

Homomorphisms on holomorphic functions in infinite dimensions
Speaker: Richard M. Aron (Kent State Univ., USA)

i-Fitting-Formations on Clifford semigroups
Speaker: Ana Catarina Monteiro (CEMAT, Univ. Lisboa)
In this talk, we will explore the concept of i-Fitting-Formation of Clifford semigroups. A Clifford semigroup is an inverse semigroup that is a union of groups. A class of Clifford semigroups is an i-formation if it is closed for idempotent separating quotients and for finitary...

More than perfect but not perfect enough
Speaker: Maria João Gouveia (CEMAT, Univ. Lisboa)
We start by presenting a brief overview of the various known lattice representations.  From there we introduce some results of our work on TiRS graphs which abstract the lattice duals in Ploscica's representation (1995) via maximal partial maps into the two-element set. Those particular...

Structure of quasi-crystal graphs and applications to the combinatorics of quasi-symmetric functions
Speaker: Inês Rodrigues (Univ. Nova de Lisboa)
Crystal graphs are powerful combinatorial tools for working with the plactic monoid and symmetric functions. Quasi-crystal graphs are an analogous concept for the hypoplactic monoid and quasi-symmetric functions.We explicitly describe a previously observed isomorphism of components of the...

Delsarte's extremal problem and packing on locally compact Abelian groups
Speaker: Elena Berdysheva (Univ. Cape Town, South Africa)

An approach to the solvability of a fractional differential problem
Speaker: Anabela Silva (Univ. Aveiro)

"Classical" orthogonal polynomials of more than one variable
Speaker: Yuan Xu (Univ. of Oregon, USA)

On \(C^2\)-actions on complex surfaces
Speaker: Aram Diaw (CMUP, Univ. Porto)
Given a complex surface \( S \), we are interested in the description of an \( C^2 \)- action on \( S \).  It is well-known that this kind of action can be seen as the group of transformations given by the global flows of a pair of commuting complete vector fields. Our goal is to...

Torsionfree representations of Smith algebras
Speaker: Samuel Lopes (CMUP, Univ. Porto)
We will discuss representations of the Smith algebra which are free of finite rank over a subalgebra which plays a role analogous to that of the (enveloping algebra of the) Cartan subalgebra of the simple Lie algebra \( \mathfrak{sl}_2 \). In the case of rank 1, we obtain a full description...

Discrete harmonic analysis related to classical orthogonal polynomials
Speaker: Alberto Arenas (University of La Rioja, Spain)

On the structure of the infinitesimal generators of semigroups with discrete Lyapunov functionals
Speaker: Carlos Rocha (Instituto Superior Técnico, Lisbon)
Dynamical systems generated by scalar reaction-diffusion equations enjoy special properties that lead to a very simple structure for the semiflow. Among these properties, the monotone behavior of the number of zeros of the solutions plays an essential role. This discrete Lyapunov functional...

Standard monomials and Gröbner bases of positroid varieties
Speaker: Daoji Huang (Univ. MInnesota, USA)
Influential work of Hodge from the 1940s led the way in using Gröbner bases to combinatorially study the Grassmannian. In this talk, we will follow Hodge's approach in order to investigate certain subvarieties called positroid varieties. Positroid varieties, introduced by Knutson-Lam-Speyer...

Mordell-Tornheim zeta functions, Hurwitz lift and functional equations of Herglotz-Zagier type functions
Speaker: Atul Dixit (Indian Institute of Technology Gandhinagar)

An adjoint theorem for finitary functors
Speaker: Lurdes Sousa (CMUC and IP Viseu)
A functor between locally presentable categories is a right adjoint iff it is accessible and preserves limits [1]. We prove that for a number of categories, called graduated, the preservation of countable limits is enough. Examples of graduated categories include sets, posets, Boolean...

Predicate liftings and lax extensions of functors
Speaker: Dirk Hofmann (CIDMA, Univ. Aveiro)
Lax extensions of SET-functors to bicategories of (enriched) relations are a well-established tool in various parts of mathematics: they are fundamental in our work on "monoidal topology", but also generic notions of bisimulation for coalgebras rely on identity-preserving (=normal) lax...

The Schrödinger equation for the Rosen-Morse type potencial revisited with applications
Speaker: Guillermo Gordillo-Núñez (CMUC, UC|UP PhD student)

A review on the Eulerian ideal of a graph and its regularity
Speaker: Gonçalo Varejão (CMUC, UC|UP PhD student)
Over the past fifty years, a trend in commutative algebra has been to explore families of homogeneous ideals, in the polynomial ring, linked to various combinatorial structures, such as graphs, hypergraphs and simplicial complexes.In this presentation, we focus on the Eulerian ideal of a...

A characterization of one-element commutation classes
Speaker: Diogo Soares (CMUC, UC|UP PhD student)
A reduced word for a permutation of the symmetric group is its own commutation class if it has no commutation moves available. These words have the property that every factor of length 2 is formed by consecutive integers, but in general words of this form may not be reduced.  In this...

Lie groupoids: between equivariant and non-commutative geometry
Speaker: Bjarne Kosmeijer (Univ. Amsterdam, Netherlands)
Lie groupoids are important objects in the study of symmetries, because they encode a broader notion of symmetries than just actions of Lie groups. It is important, for instance in the context of index theory, to understand the equivariant geometric aspects of a Lie groupoid. For Lie...

Supercharacters: behind and beyond
Speaker: Carlos André (CMUC & Univ. Lisboa)
Describing the conjugacy classes or irreducible characters of the unipotent upper triangular group over a finite field is known to be an impossibly difficult problem. Superclasses and  supercharacters have been introduced (under the names of "basic varieties" and "basic characters") as...

The dichotomy between enriched and internal categorical structures
Speaker: Rui Prezado (CMUC, Univ. Coimbra)
We revisit the dichotomy between enriched and internal categories in a base category V. By describing these objects as monads internal to certain proarrow equipments, we construct a change-of-base adjunction between the category of enriched V-categories and the category of internal...

Effective descent morphisms of Ord//X, revisited
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
In this talk we will present recent results on effective descent morphisms of the lax comma category Ord//X, which improve results obtained in [2]. While in [3] effective descent morphisms of Ord, and consequently of the comma category Ord/X, were obtained making use of the category of...

Exploring variations of Carleson's Problem
Speaker: Shobu Shiraki (Instituto Superior Técnico, Lisboa)
Carleson's problem in harmonic analysis investigates the minimal smoothness required in initial data to ensure almost everywhere convergence in Schrödinger equation solutions. Here, we study two recent variants of the problem: convergence along a curve and convergence for infinitely many...

CMV bispectrality of Baxter's biorthogonal polynomials and affine Hecke algebra
Speaker: Alexei Zhedanov (Renmin University of China)

On special positive solutions of the first discrete Painlevé hierarchy
Speaker: Ana Filipa Loureiro (University of Kent, UK)

Viscosity Comparison Theorem for second order spider HJB equations having a "local-time" Kirchhoff's boundary transmission
Speaker: Isaac Ohavi (Hebrew Univ. of Jerusalem, Israel)
We start this talk by recalling briefly the last results I have obtained on Walsh spider diffusion having a spinning measure selected from the own local time spent by the process at the vertex. We emphasize the key "non-stickiness" property of the process at the junction point, which...

Pontryagin's Maximum Principle for optimization in random environments
Speaker: Joshué Helí Ricalde-Guerrero (CIMAT, Guanajuato, Mexico)
One of the primary methods for solving optimization problems involves determining a set of necessary conditions for any optimal solution. These conditions can become sufficient under additional convexity assumptions on the objective/constraint functions. Pontryagin's Maximum Principle (PMP)...

Reduction by symmetry in Riemannian homogeneous spaces with applications to path-planning
Speaker: Jacob Goodman (Nebrija Univ., Spain)
In this talk, we derive the necessary conditions for optimality in a second-order variational problem on Riemannian homogeneous spaces by making use of the second fundamental form, reinterpreted as a connection on a horizontal distribution on the underlying Lie group. We assume that the...

Geometric integrators for Riemannian cubic splines
Speaker: Alexandre Anahory Simões (IE School of Science and Technology, Spain)
Riemannian cubic polynomials are a generalization of splines to Riemannian manifolds with applications in optimal control problems and interpolation problems. Riemannian cubic polynomials are obtained as the curves minimizing a higher-order functional depending on the covariant acceleration...

Classical and semi-classical orthogonal polynomials on lattices
Speaker: Dieudonné Mbouna (Univ. Sevilla, Spain)

A bi-equivalence for topoi with enough points
Speaker: Joshua Wrigley (Univ. degli Studi dell'Insubria, Como, Italy)
Grothendieck topoi and geometric morphisms generalise topological spaces and continuous maps.  Loosely speaking, a topos can be viewed as a space where the points have been endowed with the extra structure of a space of isomorphisms between points, that is, a topological...

Adjoint split extensions and 2-dimensional protomodularity
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
There are a number of constructions involving categories that behave similarly to semidirect products of groups. These include Artin glueings of frames (viewed as thin categories) or toposes, and the decomposition of the category of cocommutative Hopf algebras (over a field of characteristic...

Structure-preserving integrators in Poisson geometry
Speaker: Oscar Cosserat (Univ. Gottingen, Germany)
A geometric integrator is a numerical method that preserves the geometric properties of the flow of a differential equation. The rise of geometric integrators stems from the geometrization of mechanics and the development of numerical analysis. I will explain here their relevance within the...

Hydrodynamic limit of the multi-component slow boundary WASEP with collisions
Speaker: Oslenne Nogueira Araújo (CMUC)
In this joint work with Patrícia Gonçalves (IST-ULisboa) and Alexandre Simas (KAUST), we study the hydrodynamic limit for a stochastic interacting particle system whose dynamics consists of a superposition of several dynamics:  the exclusion rule, that dictates that no more than a...

Duality for transitive partial CABAs
Speaker: Rui Soares Barbosa (Iberian Nanotechnology Laboratory, Braga)
joint work with Samson Abramsky (UCL).Partial Boolean algebras (pBAs) were introduced by Kochen and Specker in  their seminal work on contextuality, a key signature of non-classicality  in quantum mechanics which has more recently been linked to quantum  computational...

Unraveling the iterative chad
Speaker: Fernando Lucatelli Nunes (CMUC & Utrecht Univ., Netherlands)
Reverse mode Automatic Differentiation (AD), a fundamental technique harnessing the chain rule to compute derivatives of functions implemented by programs, plays an integral role in addressing the challenges of efficiently computing derivatives of functions with high-dimensional domains...

Weyl-algebraic approach to special functions: a case of study
Speaker: Edmund YM Chiang (The Hong Kong University of Sciences and Technology)

A brief introduction to Machine Learning: from the perceptron to large language models
Speaker: Francisco Pereira (CISUC & Polytechnic Institute of Coimbra)
The field of machine learning has experienced a strong expansion in recent years, mostly driven by the development of new computational methods and the unprecedented surge in the volume of data accessible for processing and analysis. This dynamic has opened up new frontiers for exploration...

Existence and interior regularity of solutions of a fully nonlinear transmission problem
Speaker: David Stolnicki (Technion - Israel Institute of Technology, Haifa)
Our study delves into the existence and regularity of  transmission problems represented by the equation \( \sigma_i(Du)  F(D^2u)=f \), concerning regions where \(u>0\) and \(u<0\). This work solves  the question on existence of solutions for the problem by utilizing a...

On derived functors of semimodule-valued functors
Speaker: Alex Patchkoria (A. Razmadze Math. Institute of Tbilisi State Univ., Georgia)
A concept of a proper projective semimodule is introduced and proper projective resolutions are used to construct derived functors of additive functors from the category of cancellative semimodules to the category of cancellative semimodules. We investigate exactness of the long sequence of...

Uniform completions via Cauchy sequences
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
While the usual approach using Cauchy sequences is not powerful enough to give completions of uniform spaces in general, if handled appropriately Cauchy sequences suffice for completions of uniform locales. We describe the construction and talk about how this approach might be applied more...

Induced congruences in \(\sigma\)-frames
Speaker: Raquel Bernardes (CMUC, Univ. Coimbra)
Given a \( \sigma \)-space \( X \) and its lattice of open sets \( \mathcal{O}(X) \), we will study congruences on the \( \sigma \)-frame \( \mathcal{O}(X) \) representing the subspaces of \( X \) (referred to as induced congruences). We will show that when \( X \) is a \( T_D \) \(...

Discrepancy of stratified samples from partitions of the unit cube
Speaker: Florian Pausinger (Queen's Univ. Belfast, Northern Ireland)
Jittered sampling is a classical way of generating structured random sets in a d-dimensional unit cube. Such sets combine the simplicity of fixed grids with certain probabilistic properties of sets of i.i.d uniformly distributed points and are thus a popular choice in numerical...

On the Dorfman connections of a Courant algebroid
Speaker: Fani Petalidou (Aristotle Univ. Thessaloniki, Greece)
In this talk, after a short introduction to Courant algebroids and the related algebras defined by them, we will present the notion of Dorfman connection of a Courant algebroid on a vector bundle and some basic results about this. Then, we will present the role of such connections in...

Dynamics and stability of a network human-landscape model
Speaker: Ana Jacinta Soares (CMAT, Univ. Minho)
Ecological networks serve as a modern tool to explore the dynamics of interconnected, non-uniform landscape regions. We develop a mathematical model by coupling human activity with an ecological model for a network of Landscape Units (LUs). The model consists of a network of interacting...

On the embedding between variable Lebesgue space \(L^{p(\cdot)}(\Omega)\) and \(L(LogL)^{\alpha}(\Omega)\) space
Speaker: Amiran Gogatishvili (Czech Academy of Sciences, Prague, Czech Republic)
We give some sufficient conditions on distribution \( |\{x\in \Omega :\,p(x)\leq 1+\lambda\}|\,(\lambda>0) \) of the exponent function \( p(\cdot): \Omega \to [0,\infty) \) that implies the embedding \( L^{p(\cdot)}(\Omega)\subset L(LogL)^{\alpha}(\Omega)\,(\alpha>0) \),...

Advances in finite volume methods for the simulation of flows in porous media
Speaker: Fernando Raul Contreras (Univ. Federal de Pernambuco, Brazil)
We study linear and nonlinear finite volume methods coupled to the high order methods to simulate the behavior of flows in porous media with complex geological properties. Ideally, the linear and nonlinear methods should satisfy the following numerical properties: Preserve linearity, handle...

Coagulation equations with source leading to anomalous self-similarity
Speaker: Eugenia Franco (Univ. of Bonn, Germany)
Smoluchowski's coagulation equation describes the evolution in time of a system of atmospheric particles, coagulating upon binary collision. In this talk I will present a generalization of the classical Smoluchowski's coagulation equation, i.e. the coagulation equation with a source term of...

More on descent theory of closure spaces and related remarks
Speaker: Manuela Sobral (CMUC, Univ. Coimbra)
By a closure space we mean a set equipped with a closed under intersections set of its subsets. The purpose of this talk is to briefly recall our recent results on descent theory of closure spaces, and consider their E-versions, where E consists either of closed or of open maps, comparing...

Inverse semigroup cohomology and crossed module extensions of semilattices of groups by inverse semigroups
Speaker: Mykola Khrypchenko (Univ. Porto)
We introduce the notion of a crossed module over an inverse semigroup which generalizes the notion of a module over an inverse semigroup in the sense of Lausch [1], as well as the notion of a crossed module over a group in the sense of Whitehead [4] and Maclane [3]. With any crossed \( S...

Cumulant hierarchy and chaos in the Kac model
Speaker: Aleksis Vuoksenmaa (Univ. of Helsinki, Finland)
Kac's (stochastic) model describes the time-evolution of the velocities of homogeneously situated particles that, upon random binary collision, redistribute their kinetic energies in a way that conserves the total energy of the many particle system. In this joint work with Jani Lukkarinen,...

Coagulation equations from applications: existence and mass conservation
Speaker: Sakari Pirnes (Univ. of Helsinki, Finland)
The Smoluchowski coagulation equation is considered to be one of the most fundamental equations of the classical description of matter alongside the Boltzmann, Navier-Stokes and Euler equations. In this talk, we consider measure valued solutions to multicomponent coagulation equation and...

Localization in multicomponent coagulation systems
Speaker: Marina Ferreira (CMUC, University of Coimbra)
We study the properties of multicomponent Smoluchowsky coagulation equations. These equations describe the evolution of the number density function over the high-dimensional particle composition space. We show that, under a self-similar scaling, all solutions localize along a line defined by...

Fully nonlinear equations degenerating as a Muckenhoupt weight
Speaker: David Jesus (Univ. of Bologna, Italy)
We will discuss the regularity of viscosity solutions for fully nonlinear Hessian equations with coefficients in some Muckenhoupt class. We prove Holder and higher regularity under mild assumptions on the coefficients. We use approximation techniques in the spirit of Caffarelli's seminal...

Volume bounds on canonical lift complements of random geodesics
Speaker: Didac Martinez Granado (Univ. of Luxembourg)
Given a filling closed geodesic on a hyperbolic surface, one can consider its canonical lift in the projective tangent bundle. Drilling this knot, one obtains a hyperbolic 3-manifold. In this talk we are interested in volume bounds for these manifolds in terms of geometric quantities of the...

Exploring polynomial equations through Field Theory
Speaker: Sophie Marques (Stellenbosch Univ., South Africa)
In this talk, we explore the intricate connections between polynomial equations, field theory, and the fascinating realm of roots of unity. Drawing on recent research advancements, we will present compelling examples that illustrate the significance of our collaborative work with Kenneth...

Topology and topoi via internal groupoids
Speaker: Norihido Yamada (Univ. do Minho)
Modern game semantics grew out of the full completeness problem for linear logic and the full abstraction problem for PCF, and more recently it has been applied to the study of type systems and programming languages. My past work took a new direction by developing game semantics into a model...

Boundary weak Harnack estimates and regularity for elliptic PDE in divergence form
Speaker: Fiorella María Rendón García (CMUC, Univ. Coimbra)
See attached file....

Improved regularity for a Hessian-dependent functional
Speaker: Vincenzo Bianca (CMUC, Univ. Coimbra)
We prove that minimizers of the \( L^d \)-norm of the Hessian in the unit ball of \( \mathbb{R}^d \) are locally of class \( C^{1,\alpha} \). Our findings extend previous results on Hessian-dependent functionals to the borderline case and resonate with the Holder regularity theory available...

A lattice-theoretic approach to submodular mean field games based on stochastic orders
Speaker: Max Nendel (Univ. of Bielefeld, Germany)
We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models, where data may not be continuous with respect to the measure parameter and common noise is...

From Lie algebra crossed modules to tensor hierarchies, and beyond
Speaker: Sylvain Lavau (Aristotle Univ. of Thessaloniki, Greece)
Gauging procedures in supergravity theories depart from classical gauge theories as in the former, the gauge fields take values in the fundamental representation V of the Lie algebra g of global symmetries of the system. The consistency of the theory relies on a pairing V\( \to \)g called...

The Keel-Tevelev embedding of \(M_{0,n}\)-bar
Speaker: Jake Levinson (Simon Fraser Univ., Canada)
The moduli space \( M \)\( _{0,n} \)-bar describes n-marked stable curves of genus zero. It has a closed embedding into a product of projective spaces \( P^1 \times\cdots\times P^{n-3} \), due to Keel-Tevelev and Kapranov and involving the  tautological "psi" and "omega" divisor...

Non occurrence of Lavrentiev Phenomenon for functionals with non standard growth
Speaker: Filomena De Filippis (Univ. of L'Aquila, Italy)
See attached file....

Flipping regularity and fully nonlinear equations with unbounded ingredients
Speaker: Filipe Gomes (University of Coimbra)
Our work resonates in the context of nonlinear elliptic problems, including supersolutions to fully nonlinear elliptic equations and viscosity classes. The main goal of our research is to generalize recent results for equations in which the ingredients are merely unbounded. In particular, we...

Shifted contact structures
Speaker: Luca Vitagliano (Univ. of Salerno, Italy)

On pseudo-Euclidean Lie algebras whose Levi-Civita product is left Leibniz
Speaker: Said Benayadi (Univ. of Lorraine, France)
We study a class of Lie algebras which contains the class of quadratic Lie algebras and the class of Milnor Lie algebras, namely, Lie algebras endowed a pseudo-Euclidean metric such its Levi- Civita product is left Leibniz. We call them Levi-Civita left Leibniz Lie algebras LCLL for short....

Boundedness and regularity of the solutions of a kind of nonlinear systems
Speaker: Lubomira Softova (Univ. of Salerno, Italy)
See attached file....

A low-cost algorithm to determine spacecraft trajectories in CR3BP
Speaker: Sirani M. Perera (Embry-Riddle Aeronautical University, USA)
The traffic within the Cislunar region continues to grow, yielding an increasing demand for efficient techniques to determine the trajectory of a satellite in the circular restricted three-body problem (CR3BP). In this talk, we introduce a novel technique that incorporates interpolation with...

Non symmetric Cauchy kernel, crystals and last passage percolation
Speaker: Olga Azenhas (CMUC, Univ. Coimbra)
We use non-symmetric Cauchy kernel identities to get the law of last passage percolation (LPP) models in terms of Demazure characters (which are non symmetric polynomials) of a gl_n Lie algebra. The construction is based on  restrictions of the Robinson-Schensted-Knuth (RSK)...

Blocks of endomorphism algebras of Young permutation modules for Hecke algebras
Speaker: Stephen Donkin (Univ. of York, UK)
We consider a symmetric group acting on a set whose  point stabilisers are products of smaller symmetric group (more precisely Young subgroups). The corresponding permutation module is called a Young permutation module. Familiar examples such as  group algebras of symmetric groups,...

Varieties of algebras with derivations
Speaker: Carla Rizzo (Univ. degli Studi di Palermo, Italy)
See attached file....

A new characterization of internal groupoids
Speaker: Nelson Martins-Ferreira (IP Leiria)
In this talk we will present a new characterization of internal groupoids using involutive-2-links. An involutive-2-link consists of a single morphism equipped with a pair of interlinked involutions on its domain [1]. We will see that there exists a full and faithful functor from the...

Higher-order quantitative equational theories
Speaker: Renato Neves (Univ. do Minho)
Modern universal algebra frequently involves notions of equality that go beyond  the standard binary setting, in which equality either holds or does not hold. In this talk we explore the idea of equality taking values from a quantale V, which covers the cases of (ultra)metric,...

Logical pluralism
Speaker: Vincenzo Fano (Univ. Urbino, Italy)
The seminal book on logical pluralism written by Beall and Restall (2006) is discussed. The most relevant scholarly literature on the topic is critically presented. A more syntactical form of logical pluralism is defended. In particular, it is shown that the question of logical pluralism...

Towards a general obstruction theory for geometric structures?
Speaker: Giorgio Trentinaglia (CAMGSD, Univ. Lisboa)
Explicit criteria for the existence of geometric structures on manifolds are known in specific cases and may be understood as special solutions to a certain problem in classical obstruction theory. Adopting Cartan's (and Ehresmann's) views on differential geometry, geometric structures may...

The localic groupoid classifying a geometric theory
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
Famously, Joyal and Tierney proved that every Grothendieck topos can be represented as a topos of equivariant sheaves over a localic groupoid. Hence, toposes can be understood as ‘locales plus automorphisms’. However, it appears that non-experts are often unsure about exactly how...

The lax comma category Cat//X
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
We will analyse the behaviour of the lax comma category Cat//X, for a given category X. This talk is based on ongoing joint work with Fernando Lucatelli Nunes....

Chains and covers in K-theoretic multiplication rules
Speaker: Mojdeh Tarighat (Univ. of Virginia, USA)
In 2020, Morse, Blasiak, and Seelinger introduced the K-theoretic Catalan functions as motivated by the search for a K-theoretic counterpart to the relationship between k-Schur structure constants and the complete flag variety. The authors conjectured that a subfamily, the closed k-Schur...

Regularity for fully nonlinear elliptic equations via the fractional Laplacian
Speaker: Makson Santos (Instituto Superior Técnico, Lisboa)
In the presence of unbounded source terms, we study high-order fractional Sobolev regularity for fully nonlinear, uniformly elliptic equations. Our techniques are based on touching the solution with C1,α cone-like functions to produce a decay rate of the measure of certain sets,...

A multiphase shape optimization problem with measure constraint
Speaker: Pêdra Andrade (Instituto Superior Técnico, Lisboa)
We study a class of optimal partition problems with measure constraints. We establish the existence of the optimal partition by using a weak formulation that involves a minimization problem where the variables are functions rather than domains. Then, we also prove that...

Statistical enumeration of groups by double cosets
Speaker: Persi Diaconis (Stanford Univ., USA)
Let H and K be subgroups of a finite group G. This divides G into H-K double cosets. One may ask (1) how many double cosets are there? (2) what are their sizes? (e.g. pick g in G at random, what double coset is it likely to be in?) (3) Can one find 'nice names' for the double cosets? (4)...

Metric Fourier approximation of set-valued functions of bounded variation
Speaker: Elena E. Berdysheva (Univ. of Cape Town, South Africa)
We study set-valued functions (SVFs) mapping a real interval to compact sets in Rd. Older approaches to the approximation of set-valued functions investigated almost exclusively SVFs with convex images (values). The standard methods suffer from convexification. In this talk I will...

Normal forms in Poisson geometry
Speaker: Ioan Marcut (Univ. Nijmegen, Netherlands)
This is an introductory talk to Poisson geometry, with a focus on normal forms for Poisson structures. First, we will discuss Weinstein's Splitting theorem and the linearization problem around points, including Conn's theorem. Then I will discuss some of the problems I have worked on:...

Exact Borel subalgebras, good quotients and good subalgebras
Speaker: Teresa Conde (Univ. of Stuttgart, Germany)
Exact Borel subalgebras of strandardly stratified algebras emulate the role of classic Borel subalgebras of complex semi-simple Lie algebras. Up to Morita equivalence, every standardly stratified algebra has an exact Borel subalgebra. By their recursive nature, standardly stratified algebras...

Polyadic sets and unnatural isomorphisms
Speaker: Luca Reggio (University College London, UK)
A polyadic set over a category C is a presheaf over C satisfying an appropriate amalgamation property. Polyadic sets are a discrete variant of Joyal's polyadic spaces, which are dual to Lawvere's Boolean hyperdoctrines. I will give an overview of some basic ideas and constructions concerning...

Van Est Theorems for Lie groupoids
Speaker: Lennart Obster (CMUC, UC|UP PhD student)

Moduli of twisted Higgs bundles as a degeneration of moduli of Lie algebroid connections
Speaker: André Oliveira (CMUP, Univ. Trás-os-montes e Alto Douro)
Out of a given holomorphic Lie algebroid L on a compact Riemann surface X, one can consider a corresponding L-connection on a vector bundle over X. This naturally degenerates onto a (twisted) Higgs bundle on X. Via a generalization of the classical construction by Simpson of...

Groebner Basis
Speaker: Alexander Kovacec (CMUC, Univ. Coimbra)

A gentle introduction to the Hitchin fibration
Speaker: Juan Sebastian Numpaque (CMUP, UC|UP PhD student)

What are Lie algebroids and Lie algebroid connections?
Speaker: João Nuno Mestre (CMUC, Univ. Coimbra)

When are there enough isomorphisms? Representing theories by groupoids of models
Speaker: Joshua Wrigley (Università degli Studi dell'Insubria, Como, Italy)
For some logical theories, the data of the theory can be reconstructed from the group of automorphisms of a "special model". For example, the theory of dense linear orders can be reconstructed from the automorphism group of the rationals (considered as a dense linear order). ...

Transverse densities and modular classes of Lie groupoids
Speaker: João Nuno Mestre (CMUC, Univ. Coimbra)
The modular class of a Lie groupoid is a generalization of the modular class of a Lie group, which detects the failure of the Haar measure to be bi-invariant.Certain (good) functors on vector spaces, for example volume elements, and densities, lead to 1-dimensional representations of Lie...

Variational solution to Bernoulli type free transmission problems
Speaker: Harish Shrivastava (Tata Institute of Fundamental Research, Bangalore, India)
In this seminar, I will discuss the regularity theory and some aspects related to free boundaries of variational solutions to Bernoulli type free transmission problems. We start with discussing challenges which come while proving optimal regularity of minimisers when coefficients are only...

Crystals, and the Berenstein-Kirillov, cacti and related groups
Speaker: Olga Azenhas (CMUC, Univ. Coimbra)
Berenstein and Kirillov have introduced and studied the group generated by the Bender-Knuth involutions modulo the relations they do satisfy on semi-standard tableaux of straight shape. Halacheva has generalized the Henriques-Kamnitzer cactus group to Dynkin diagrams of classical Cartan...

Some aspects of enriched completely distributive lattices
Speaker: Dirk Hofmann (CIDMA, Univ. Aveiro)
The topics of this talk are motivated by two classic results: firstly, the fact that "Topop is a quasi-variety" proven by Barr and Pedicchio in 1995; secondly, the identification of (constructively) completely distributive lattices as the nuclear objects in the autonomous category...

Pervin spaces and Frith frames: bitopological aspects and completion
Speaker: Célia Borlido (CMUC, Univ. Coimbra)
A Pervin space is a set equipped with a bounded sublattice of its powerset, while its pointfree version, called Frith frame, consists of a frame equipped with a generating bounded sublattice. It is known that the dual adjunction between topological spaces and frames extends to a dual...

(Quasi)-Painlevé equations and Painlevé equivalence problem
Speaker: Galina Filipuk (Univ. of Warsaw, Poland)
Painlevé equations are second order nonlinear differential equations solutions of which have no movable critical points (algebraic singularities). They appear in many applications (e.g., in the theory of orthogonal polynomials) but in disguise. How to find a transformation to the...

Extremal index and periodicity for chaotic dynamical systems
Speaker: Ana Cristina Freitas (CMUP, Univ. Porto)
The extremal index appears as a parameter in Extreme Value Laws, characterising the clustering of extreme events. We apply this idea to a dynamical systems context to analyse the possible extreme value laws for the stochastic process generated by observations taken along dynamical orbits. We...

Computing generalized Seifert matrices for closures of colored braids
Speaker: José Pedro Quintanilha (Univ. Bielefeld, Germany)
Seifert matrices have been a foundational tool in knot theory ever since they were introduced in the 1930's. They are not link invariants - in fact, the definition of a Seifert matrix for a link L depends heavily on the choice of a Seifert surface S for L and of a Z-basis of H_1(S)....

Tropicalizing moduli spaces
Speaker: Margarida Melo (U. Roma Tre / CMUC)
In algebraic geometry, the existence of moduli spaces to parametrize certain classes of objects is of central importance. Moreover, since these moduli spaces are often not compact, the construction of modular compactifications for theses spaces is very useful, as one can study them by using...

On the holonomy group
Speaker: Hamza Bakhouch (UC|UP PhD student)
In differential geometry, a differential structure on a topological space allows us to see locally our space like a Euclidean space. A foliation structure on a differential manifold allows us to see the manifold, locally as a family of "horizontal" (lines/planes/hyperplanes...) and...

On lax comma categories of ordered sets
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
We will analyse the behaviour of the lax comma category Ord//X, for a complete ordered set X, namely with respect to exponentiability and descent.This talk is based on joint work with Fernando Lucatelli Nunes....

Descent for split fibrations
Speaker: Fernando Lucatelli Nunes (Utrecht Univ. & CMUC)
See attached file....

Examples of explicit solutions to the cubic wave equation
Speaker: Giuseppe Negro (CAMGSD, IST)
We construct a two-parameter family of solutions to the focusing cubic wave equation in $\mathbb{R}^{1+3}$. Depending on the values of the parameters, these solutions either scatter to linear ones, blow-up in finite time, or exhibit a new type of unstable behaviour that acts as a threshold...

The congruent number problem
Speaker: Nirina Albert Razafimandimby (UC|UP PhD student)
In mathematics, especially in number theory, we often encounter problems that are easy to state, but whose solution is often extremely difficult and sometimes requires sophisticated methods from other branches of mathematics. The Congruent Number Problem is one such unsolved problem that...

Solving integro-differential problems with the Tau method: TauToolbox
Speaker: Paulo Vasconcelos (CMUP, Univ. Porto)
The spectral Tau method delivers polynomial approximations to the solution of differential problems. The method tackles both initial and boundary value problems with ease and ensures excellent error properties, whenever the solution is smooth.In this talk, the Lanczos' Tau method is examined...

The palindromization map
Speaker: Dominique Perrin (Univ. Gustave-Eiffel, Paris-Est, France)
The palindromization map has been defined initially by Aldo de Luca in the context of Sturmian words. It was extended to the free group of rank 2 by Kassel and Reutenauer. We extend their construction to arbitrary alphabets. We also investigate the suffix automaton and compact suffix...

Scientific machine learning: some methods and applications

Emmanuel Franck & Victor Michel-Dansac (Inria & IRMA, Strasbourg, France)

Machine learning performance has exploded since the beginning of the 2010s. In this talk, we propose to investigate what learning can bring in the context of scientific computing and approximation of PDEs. To that end, we will introduce two interesting frameworks:...

A characterisation of Lie algebras using ideals and subalgebras
Speaker: Xabier García Martínez (Univ. Vigo, Spain & Vrije Universiteit Brussel, Belgium)
In this talk we will state a result characterising the variety of Lie algebras amongst all varieties of non-associative algebras. More specifically, the variety of Lie algebras is the only variety that simultaneously satisfies the following two properties: every subalgebra of a free algebra...

Mathematical modeling and numerical simulation in stimuli responsive drug delivery systems
Speaker: José Augusto Ferreira (CMUC, Univ. Coimbra)
Stimuli responsive drug delivery systems are medical devices that are able to deliver drugs locally in the target tissue in a controlled way and without affecting the healthy tissues. The drugs are encapsulated in nanostructures that able to be safely transported to the target tissue where...

Scalable methods for high-dimensional inverse problems using neural networks and implicit method of moments
Speaker: João M. Pereira (IMPA, Rio de Janeiro, Brazil)
I will talk about two recent projects of mine in that concern high-dimensional inverse problems. In the first project, we use machine learning tools for discovering laws and equations that govern high-dimensional datasets. Specifically, I will present two methods we...

The homology language of a higher-dimensional automaton
Speaker: Thomas Kahl (CMUM, Univ. Minho)
Higher-dimensional automata, i.e., labeled precubical sets, are a very expressive combinatorial-topological model for concurrent systems. In this seminar, I will talk about the homology language of a higher-dimensional automaton, which is defined as the image of a labeling homomorphism from...

Identities and bases in hypoplactic, sylvester and Baxter monoids
Speaker: Duarte Ribeiro (CMA, Univ. Nova de Lisboa)
See the attached file....

Duality: from theory to applications
Speaker: Célia Borlido (CMUC, Univ. Coimbra)
In 1936, Marshall H. Stone proved the so-called Stone's representation Theorem for Boolean algebras, thus establishing a duality between Boolean algebras and certain topological spaces. Inspired by Stone's result, many dualities between suitable categories of topological spaces and of...

An introduction to the localic approach to topology
Speaker: Jorge Picado (CMUC, Univ. Coimbra)
A topological space is a set of points along with a topology, a system of subsets called open sets that with the operations of union (as join) and intersection (as meet) forms a lattice with certain properties. In the localic approach to topology one forgets about points and thinks about a...

Riemann surfaces, line bundles and divisors
Speaker: Gabriel Martinho (UC|UP PhD student)
Line bundles are fundamental objects in geometry, generalizing some properties of tangent and cotangent bundles of manifolds. In algebraic geometry, it is common to consider line bundles over compact Riemann surfaces. On the other hand, it is also frequent to make use of divisors on these...

Weighted inequalities restricted on the cone of monotone functions and applications in the real interpolation
Speaker: Amiran Gogatishvili (Czech Academy of Sciences, Prague, Czech Republic)
We consider Hardy inequalities restricted on the cone of monotone and quasi-concave functions and we will give applications of this in the embedding of Lorentz-type spaces and in the real interpolation.  Link to access the seminar via...

Completeness and linearization
Speaker: Matias del Hoyo (Univ. Federal Fluminense, Brazil)
Given a surjective submersion, the following are equivalent: (i) it is locally trivial, (ii) it admits a complete connection, (iii) it admits a fibered complete metric. Surjective submersions are examples of Lie groupoids, and conversely, any Lie groupoid can be regarded as a surjective...

Digging into fractional diffusion equations
Speaker: Ercília Sousa (CMUC, Univ. Coimbra)
Diffusion models, involving differential equations with non-integer order derivatives, have lately become extremely popular because it is believed they can describe the observed reality more accurately than models based on integer order derivatives. They have been appearing in several...

Wave propagation in viscoelastic materials
Speaker: Afonso Costa (UC|UP PhD student)
Here we present a study of a problem that describes the displacement of a wave in a viscoelastic material. To the problem are established existence, uniqueness and stability results. Furthermore, a numerical method is proposed, a semi-discrete defined over a non-uniform partition and the...

Alternative algebras and maps preserving products equal to fixed elements
Speaker: Douglas de Araujo Smigly (Univ. São Paulo, Brazil)
See the attached file...

Profinite codes
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
A code over the alphabet A is a nonempty subset of the free monoid over A that freely generates a free submonoid.In this talk we review some results about the topological closure of codes over A in the free profinite monoid generated by A, and present some applications of such closures to...

Taking verifiability seriously
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
Interpreting open sets as verifiable properties and continuous functions as processes helps explain many aspects of topology. However, it might appear that taking this approach completely seriously sometimes leads to conclusions that contradict known results. For instance, it might seem that...

High order methods for PDE: panorama and perspective
Speaker: Stéphane Clain (CMUC, Univ. Coimbra)
Very high order methods enable to substantially reduce the computational effort while producing high accuracy approximations. They also provide high spectral resolution to catch very small structures with respect to the mesh parameter size. Three major issues have to be addressed to ...

Dirac structures and Hamiltonian inverse problem, applications to linear systems and Lotka-Volterra equations
Speaker: Hassan Alishah (Univ. Minas Gerais, Brazil)
In this talk, I, first, will provide some preliminary definitions and observations on Dirac/big-isotropic structures and Hamiltonian inverse problem. Then I will present an algorithm to solve the Hamiltonian inverse problem for a given system written in the gradient form. Then I will discuss...

Hamilton's equations and symplectic numerical methods
Speaker: Gonçalo Oliveira (UC|UP PhD student)
Hamilton's equations can be used to model many problems in the real world, and these equations could present several properties. Thus, in this talk, we are going to study numerical methods that preserve such properties, such as the Symplectic Euler Method. ...

Category Theory: history, basics and monads
Speaker: Federico Rizzetto (UC|UP PhD student)
The aim of my seminar is to present a brief introduction to basics in category theory and to quote some applications of it. Precisely my seminar is divided into four parts. Some lines of the history of category theory, a quoting of some applications in several branches of mathematics, a...

Improved regularity estimates at free and fixed boundary points
Speaker: Damião J. Araújo (Univ. Federal da Paraíba, Brazil)
We will discuss local regularity versus regularity estimates at free and fixed boundary points for solutions of degenerate nonlinear elliptic PDEs. We will be interested in showing how precisely the smoothness of a given solution is affected by degenerate diffusion models and free and fixed...

Modelling light propagation in the cornea
Speaker: Milene Santos (UC|UP PhD student)
To model the incidence and reflection of light in the cornea, we can use the Maxwell's equations. In this talk, we focus on the Maxwell's equations in the time-harmonic form which translates into the Helmholtz equation. We propose a numerical method based on nodal discontinuous Galerkin...

Riemann's Zeta Function
Speaker: Adriana Cardoso (UC|UP PhD student)
The Riemann's Zeta function is a very interesting mathematical object, due to its relation to the prime numbers and to the Riemann's Hypothesis, proposed in 1859 and still to this day unanswered. In this seminar, we will see some equivalents to the famous hypothesis, involving the...

3-manifolds, knots and surfaces
Speaker: João Nogueira (CMUC, Univ. Coimbra)
We will survey the motivation and history of 3-manifold topology, together with its twin subject of knot theory, giving emphasis to the importance of surfaces and groups on the understanding of these subjects. Under this framework, we will review some recent developments and guiding open...

A low-cost alternating projection approach for a continuous formulation of convex and cardinality constrained optimization
Speaker: Evelin Krulikovski (Univ. Nova de Lisboa)
We consider convex constrained optimization problems that also include a cardinality constraint. In general, optimization problems with cardinality constraints are difficult mathematical programs which are usually solved by global techniques from discrete optimization. We assume that the...

Atomic length in Weyl groups
Speaker: Thomas Gerber (EPFL, Lausanne, Switzerland)
Let W be the Weyl group of a finite or affine root system. It is well-known that the length of an element of W equals the number of its inversions.In this talk, I will introduce the notion of "atomic length" of an element of W and present some of its properties and applications in...

Symplectic cacti, virtualization and colourful reversal of Kashiwara--Nakashima tableaux
Speaker: Jacinta Torres (Jagiellonian Univ., Krakow, Poland)
I will present an explicit action of the symplectic cactus group, as defined by Halacheva for the Dynkin diagram of a finite root system, on the crystal of Kashiwara-Nakashima tableaux, in terms of the virtualization map due to Baker. Additionally, I will present a "colourful"...

The Karoubi envelope of a semigroup
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
The importance for Semigroup Theory of the Karoubi envelope of a semigroup became apparent in the 1980s with the Delay Theorem. This result fits in a framework that was since the 1960s one of the main driving forces of Semigroup Theory: the connections between semigroups and formal...

On split extensions of preordered groups
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
As shown in [1], the category OrdGrp of preordered groups and monotone group homomorphisms does not satisfy the Split Short Five Lemma, although the behaviour of split extensions in OrdGrp has some interesting facets.In this talk we will study these split extensions, focusing in particular...

Jónsson categories
Speaker: Diana Rodelo (CMUC & Univ. Algarve)
In this work we generalise Jónsson's theorem for congruence distributive varieties of universal algebras. The linear Mal'tsev condition extracted from the ternary Jónsson terms give rise to matrix conditions Jn, n ≥ 1. We characterise regular categories C which satisfy (the...

Proof of three conjectures by M.E.H. Ismail
Speaker: Dieudonne Mbouna (University of Almeira, Spain)
In this talk we expose the theory of classical orthogonal polynomials on lattices and we use this to give positive answers to three conjectures posed by M. E. Ismail in his monograph Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005....

Translating solutions and non-parametric mean curvature flow with prescribed contact angle in Riemannian products
Speaker: Ilkka Holopainen (Univ. of Helsinki, Finland)
Abstract is attached....

Asymptotic behavior and stability of solutions in differential equations of mixed type
Speaker: Sandra Pinelas (DCEE, Academia Militar)
In this study, some new results are obtained on  stability analysis of a mixed type differential equation. These results were obtained by using an appropriate real root of the characteristic equation. Moreover, by the use of two appropriate distinct real roots of the...

On categorical conditions in the semi-abelian context
Speaker: James Gray (Stellenbosch University, South Africa)
The purpose of this talk is three-fold. To give an overview of categorical conditions that hold for the categories of groups and Lie algebras. To explain how a single categorical condition gives rise to all of these conditions. To explain which implications do and do not hold between these...

Algebraic geometry and tangent categories
Speaker: Geoff Cruttwell (Mount Allison University, Canada)
Tangent categories, first defined by Jiri Rosicky, are a categorical structure which encompasses not only ordinary differential geometry, but also synthetic differential geometry and notions of differentiation coming from computer science.In this talk, I'll discuss how the category of affine...

Combinatorial properties of link quandles
Speaker: Manpreet Singh (CAMGSD, IST, Univ. Lisboa)
Classical knot theory is the study of smooth embeddings of circles in the 3-sphere up to the ambient isotopy. One of the fundamental problems in this field is the classification of knots, for which one needs invariants. The fundamental group of a knot complement space is a...

When measurable spaces don't have enough points
Speaker: Paolo Perrone (University of Oxford, UK)
In topology, a space is called sober if every irreducible closed subset is the closure of a unique point.One can express this concept in terms of the lower Vietoris monad, which assigns to a topological space X the space HX of its closed subsets.Given a space X, we can form a parallel pair...

The definition of pre-cohesive map in perspective
Speaker: Matías Menni (Universidad Nacional de La Plata, Argentina)
Stressing topological/geometric intuition in hyperconnected geometric morphisms, we characterize the pre-cohesive ones among them. Moreover, we show that pre-cohesive maps are molecular over boolean bases....

Nonlinear smoothing by the infinite normal form reduction method
Speaker: Jorge Drumond Silva (IST, Lisboa)
Many nonlinear dispersive partial differential equations exhibit a phenomenon where the nonlinear part of the evolution, in the Duhamel integral formula, is slightly more regular than the purely linear evolution, for the same initial data. This is usually called nonlinear smoothing and is...

Artin glueings as semidirect products
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
Artin glueings provide a way to reconstruct a locale (or topos) from a closed sublocale (subtopos) and its open complement. In this talk I will explain how Artin glueings of frames can be described as weakly Schreier split extensions in the category of frames and finite-meet-preserving maps....

Terms and derivatives of polynomial functors via negation
Speaker: Charles Walker (Masaryk Univ., Brno, Czech Republic)
Given a locally cartesian closed category E with a strict initial object, we define a negation operator on E and show that this yields a dense-closed orthogonal factorization system on E.Using this negation operator (and now assuming E has disjoint finite sums) we define both terms and...

The birth of Euclidean geometry (and mathematics) & the birth of non-Euclidean geometry
Speaker: Dénes Nagy (Australian Catholic Univ., Melbourne, Australia)

On the conjugation action for quantum GL(n)
Speaker: Stephen Donkin (Univ. of York, UK)
The algebra of polynomial functions on n by n complex matrices that are constant on conjugacy classes is the free polynomial algebra on the functions giving the coefficients of the characteristic polynomial. Here we give a similar description of the algebra of invariants C(G), for the action...

Ramsey theory for infinite words
Speaker: Manuel Silva (Univ. Nova de Lisboa)
We will discuss several ramsey-type results in combinatorics on words. In one of the results, it is proved that the existence of powers or anti-powers is an unavoidable regularity for sufficiently long words. An abelian version, where we count the frequency of each letter, is conjectured to...

Lie groupoids for PDE analysis
Speaker: Ivan Beschastnyi (CIDMA, Univ. Aveiro)
Lie groupoids are effective tools for studying singular spaces, which explains their popularity in Poisson geometry, foliation theory and other fields of mathematics. They serve as natural desingularisations and come with an array of useful tools. In recent years, it was understood that...

K dissimilar paths
Speaker: Marta Pascoal (Politecnico di Milano, CMUC/University of Coimbra, and INESC Coimbra)
The aim of this talk is to address the determination of K alternative paths linking two given nodes in a network. In particular the paths are expected to minimize simultaneously a linear objective function and a similarity measure based on the overlaps between them. The problem is modelled...

Characterization of maps
Speaker: Bruno Leonardo Macedo Ferreira (Federal University of Technology-Paraná, Brazil)
See the attached file....

The Gelfand problem for the infinity Laplacian
Speaker: Fernando Charro (Wayne State University, Detroit, USA)

Ensino e Investigação de Matemática em Angola: conquistas e desafios
Speaker: Maria de Natividade (Univ. Agostinho Neto, Luanda, Angola)
Encontro com Maria de Natividade, da Universidade Agostinho Neto, Coordenadora do primeiro mestrado em Matemática em Angola. ...

Hölder and maximal regularity for Hamilton-Jacobi equations
Speaker: Marco Cirant (University of Padova, Italy)
I will discuss some results on the regularity of solutions to semilinear elliptic equations of Hamilton-Jacobi type. I will in particular focus on the Hölder regularity of solutions, and the problem of L^p maximal regularity, developing two (different?) approaches based on the Bernstein...

Associativity and the co-smash product
Speaker: Tim Van der Linden (Université Catholique de Louvain, Belgium)
The aim of this talk is to sketch some ideas in joint work-in-progress with Ülo Reimaa and Corentin Vienne. The original question we set out to answer was to characterise when the objects in a variety of algebras over a field K have a multiplication that is associative. What we found is...

An invitation to double categories and double fibrations
Speaker: Martin Szyld (Dalhousie University, Canada)
Joint work with Geoff Cruttwell, Michael Lambert, and Dorette Pronk I will present our work on the notion of fibration for double categories [*]. I will not assume prior knowledge about double categories. Instead, I will present during the talk some basic aspects of the theory of double...

Trajectory optimization in \(L^1\) and applications to some new Mean Field Games
Speaker: Filippo Santambrogio (Université Lyon 1, France)
I will present some regularity results on a variational problem for curves of probability densities where their velocity is penalized in terms of the \( L^1 \) (or total variation) norm, of the time derivative. This is motivated by a new class of Mean Field Games whose goal is to address...

Nonlocal capillarity theory
Speaker: Enrico Valdinoci (Univ. of Western Australia, Perth, Australia)
We describe some recent results motivated by a nonlocal theory of capillarity, as related to the formation of droplets due to long-range interaction potentials. We will discuss the notion of contact angle in this setting, considering a nonlocal version of the classical Young's Law, together...

A priori estimate for a fully nonlinear problem depending on the gradient
Speaker: Disson dos Prazeres (Univ. Federal de Sergipe, Brazil)
We will talk about an a priori estimate for positive solutions of some degenerate fully nonlinear elliptic equations where the nonlinearity on the RHS depends on x, u, and ∇u. As a consequence, we use the a priori estimate to establish an existence result....

Geometry of mechanical systems with constraints and impacts

Anthony Bloch (Univ. of Michigan, USA)

In this talk I will discuss some of the general theory of mechanical (Lagrangian and Hamiltonian) system on manifolds and in particular discuss how the dynamics is affected when there are nonholonomic (nonintegrable) constraints and impacts. I will discuss conservation laws, conservation of...

The combinatorics of Kostka polynomials
Speaker: Cédric Lecouvey (Univ. Tours, France)
In representation theory of the Lie algebras, each irreducible representation decomposes into weight spaces. The dimensions of these subspaces can be computed via the Weyl character formula and admit interesting quantizations. The polynomials so obtained have a simple definition and numerous...

On the existence of minimizers for Hardy inequalities
Speaker: Yehuda Pinchover (Technion, Israel Institute of Technology)
TBA      ...

Up to the boundary gradient estimates for solutions to nonlinear free boundary problems with unbounded measurable ingredients
Speaker: Diego R. Moreira (Universidade Federal do Ceará, Brazil)
In this talk, we discuss recent advances on up to the boundary gradient estimates for viscosity solutions of free boundary problems governed by fully nonlinear and quasilinear equations with unbounded coefficients. We present the new Inhomogeneous Pucci Barriers as new elements for the...

Weak adjoints and colimits in the homotopically enriched setting
Speaker: John Bourke (Masaryk Univ., Brno, Czech Republic)
In category theory, one often encounters weak colimits as well as ordinary colimits. Lack and Rosicky [1] realised that can be viewed as instances of a common concept, if we work with categories enriched over a base V equipped with an appropriate class of morphisms E. Dealing with...

In search for an algebraically sound notion of a subobject in the dual of a topos
Speaker: Zurab Janelidze (Stellenbosch Univ., South Africa)
A noetherian form over a category is a faithful bifibration over it, whose fibres are lattices, and which satisfies certain self-dual axioms ensuring the validity of homomorphism theorems (as stated relative to the form) from abstract algebra, such as the isomorphism theorems and homological...

Sublocales of the frame of fitted sublocales
Speaker: Anna Laura Suarez (Université Côte d'Azur, France)
See the attached file. ...

Functorial approach to rank functions
Speaker: Teresa Conde (Univ. of Stuttgart, Germany)
Motivated by the work of Cohn and Schofield on Sylvester rank functions on rings, Chuang and Lazarev have recently introduced the notion of a rank function on a triangulated category. A rank function is a nonnegative real-valued, additive, translation-invariant function on the objects of a...

A discrete duality for algebras of partial functions for a foundational signature
Speaker: Célia Borlido (CMUC, Univ. Coimbra)
The study of algebras of partial functions is an active area of research that investigates collections of partial functions and their interrelationships from an algebraic perspective. The partial functions are treated as abstract elements that may be combined algebraically using various...

Semibiproducts of magmas and semigroups
Speaker: Nelson Martins-Ferreira (IP Leiria)
Semibiproducts are introduced as a generalization of biproducts. Classically, biproducts are defined in the context of additive categories ([1], p. 250). The appropriate context in which the notion of semibiproduct makes sense is the one of a concrete category over sets with maps and...

Central extensions of associative algebras
Speaker: George Janelidze (University of Cape Town, South Africa)
We compare descriptions of central extensions of associative R-algebras, for a commutative ring R, defined with respect to two reflections: to R-modules (equipped with the zero multiplication) and to commutative R-algebras. In both cases, the results are as expected. However, while the first...

Multiplicative lattices, groups, braces
Speaker: Alberto Facchini (Università di Padova, Italy)
The multiplicative lattices we will consider are those defined in [Facchini, Finocchiaro and Janelidze, Abstractly constructed prime spectra, Algebra universalis 83(1) (published only in February 2022)]. Multiplicative lattices yield the natural setting in which several basic mathematical...

Recent results on planar predator-prey and competitive models with seasonality
Speaker: Carlota Rebelo Gonçalves (Univ. de Lisboa)

Minimizing movements for mean curvature flow of partitions
Speaker: Shokhrukh Kholmatov (Univ. Vienna, Austria)
In this talk I would like to discuss about a weak solution of mean curvature flow of partitions of space, defined via a minimizing movements approach introduced by Almgren-Taylor-Wang and De Giorgi. The talk is based on the joint work with Giovanni Bellettini and Antonin Chambolle....

G-structures on orbifolds
Speaker: Sebastián Daza (PhD student, CMUC)
Orbifolds allow us to model spaces like manifolds, but with good singularities on them, encoded by finite group actions. If these actions are effective, the frame bundle of an orbifold has a manifold structure. Besides, a linear geometric structure induces a symmetry (group action) on the...

Blow-ups of Lie groupoids and Lie algebroids
Speaker: Lennart Obster (PhD student, CMUC)
In the presentation, we will go into the (projective) blow-up construction for Lie groupoids and Lie algebroids. In the literature, there are different methods to be found on how to do this, especially for Lie groupoids. The main goal of the talk will be to explain the blow-up construction...

Pointwise multiplications in Morrey spaces
Speaker: Yoshihiro Sawano (Chuo Univ., Japan)
The goal of this talk is to discuss the pointwise multiplication properties of Morrey spaces. First, as a model case, we consider the Olsen inequality. Second, we discuss how to specify the pointwise multiplier spaces. Our method carries over to weak spaces. This is a joint work mainly...

Deformations of symplectic foliations via Dirac geometry and L-infinity algebras
Speaker: Alfonso Tortorella (CMUP, Univ. Porto)
In this talk, based on joint work with Stephane Geudens and Marco Zambon, we develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. The main result is that each symplectic foliation is attached with a cubic L-infinity...

Symmetric decompositions, triangulations and real-rootedness
Speaker: Eleni Tzanaki (Univ. Crete, Greece)
A triangulation of a simplicial complex Δ is said to be uniform if the f-vector of its restriction to a face of Δ depends only on the dimension of that face. The notion of uniform triangulation was introduced by Christos Athanasiadis in order to conveniently unify many well...

Topology for internal pre-orders: focus on complete regularity
Speaker: Walter Tholen (York University, Canada)
Treating the ultrafilter monad for sets as a role model, under modest hypotheses on the two parameters involved, we consider some topological notions for T-pre-orders, internal to a category C that comes equipped with a monad T. We call them T-spaces in C, present a rudimentary theory for...

Nonlinear versions of the Banach-Schauder open mapping theorem
Speaker: Sauli Lindberg (Univ. Helsinki, Finland)
I will present nonlinear versions of the Banach-Schauder open mapping theorem. They apply to constant-coefficient PDEs (and initial value problems) that are scaling-invariant and preserved under weak-* convergence. As a first application, I will present a partial result on a long-standing...

Regularity theory: from PDE to interfaces and beyond
Speaker: Edgard Pimentel (CMUC)
Operators with solution-dependent discontinuities give rise to interfaces or free boundaries. In this context, two fundamental questions appear. First, one is interested in the regularity properties of the solutions across the free boundary. Then the analysis focuses on the interfaces and...

How can the Cerebral Aneurysms near-wall region be investigated?
Speaker: Iolanda Velho (CEMAT, Univ. Lisboa)
Cerebral Aneurysms (CA) represent a frightening and silent threat with a high prevalence and mortality rate. Despite several studies, the mechanisms of aneurysm development are not fully understood. Nonetheless, hemodynamic and biochemical factors, especially related to the vessel wall, are...

Injectivity of induction in Lie theory
Speaker: Thomas Gerber (EPFL, Lausanne, Switzerland)
Given two isomorphic representations of a simple lie algebra over ℂ induced from two irreducible representations V and W of a parabolic subalgebra, what can be said about V and W? In this talk, we consider the case of the general linear and symplectic Lie algebras. We show that the...

Weak factorization systems in locally presentable categories
Speaker: Jiří Rosický (Masaryk Univ., Brno, Czech Republic)
We will deal with cofibrantly generated, accessible and fibrantly generated weak factorization systems in locally presentable categories.  The talk is mostly based on a joint work with Sean Cox. ...

Endomorphisms of hyperbolic groups
Speaker: André Carvalho (Univ. Porto, Portugal)
The Bounded Reduction Property (or Bounded Cancellation Lemma) was introduced by Cooper for automorphisms of free groups and has played an important role in the dynamical study of endomorphisms of (virtually) free groups since then.In this talk, we will present some (equivalent) geometric...

The two-sided Karnofsky-Rhodes expansion of a semigroup
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
In semigroup theory, the term "expansion" refers to an endofunctor in the category of semigroups, equipped with a natural transformation to the identity functor which is surjective in each object.There is a big number of expansions with names of semigroup theorists, a reflection of...

The notion of farness in uniform frames and its underlying Galois adjunction
Speaker: Ana Belén Avilez (PhD student, CMUC)
We will explore the notion of farness in (pre-)uniform frames and the role it plays in characterizing uniform continuity of real-valued functions. We will describe the relation of farness between elements in a frame in terms of Galois adjunctions. This will allow us to present a...

Rate of blow up in the thin obstacle problem
Speaker: Hui Yu (National University of Singapore)

Relative dominant dimension and quality of split quasi-hereditary covers.
Speaker: Tiago Cruz (Univ. Stuttgart, Germany)
Dominant dimension of a finite-dimensional algebra A is a homological invariant measuring the connection between module categories A-mod and B-mod, where B is the endomorphism algebra of a faithful projective-injective A-module.In this talk, we will discuss generalisations of dominant...

A multi-scale biological description with application to autoimmune diseases

Ana Jacinta Soares (CMAT, Univ. Minho)

Biological systems are usually described at the macroscopic level, by considering the relevant interacting populations that are involved in the system. However, it is well known that a detailed description at the cellular level could be more appropriate in understanding the complex...

Simple modules over skew polynomial rings
Speaker: Paula Carvalho (CMUP, FCUP)
We consider the structure of modules over Noetherian rings. A Noetherian ring S whose simple modules have the property that their finitely generated essential extensions are Artinian is said to satisfy property (⋄). For commutative Noetherian rings the validity of (⋄) is due to...

Non-orientable surfaces in 4-dimensional manifolds and rectangles inscribed in Jordan curves
Speaker: Peter Feller (ETH, Switzerland)
Toeplitz asked whether every Jordan curve in the Euclidean plane contains 4 points that form the corners of a square? More generally, what about the corners of a rectangle with prescribed aspect ratio? The latter question was recently answered by Greene-Lobb for smooth Jordan curves, but...

Potent preservers of incidence algebras
Speaker: Mykola Khrypchenko (Univ. Federal de Santa Catarina, Brazil)
Let X be a finite connected poset and F a field. Denote by I(X,F) the incidence algebra of X over F. We describe bijective linear maps from I(X,F) to I(X,F) which preserve k-potency, where k is a fixed integer greater than 1. The case k=2 (idempotent preservers) is treated for arbitrary F,...

A degenerate fully nonlinear free transmission problem with variable exponents
Speaker: David Jesus (PhD student, CMUC)
In this talk we will discuss optimal regularity for equations with a degeneracy rate which varies in a discontinuous fashion over the domain. Moreover, this discontinuity depends in an implicit way on the solution itself. We introduce the notion of pointwise sharp regularity which requires...

A quantum system with a non-Hermitian Hamiltonian
Speaker: Natália Bebiano (CMUC, Univ. Coimbra)
In the last decades non-Hermitian operators with real eigenvalues appeared in Quantum Mechanics (QM) and in other areas of Physics, e.g. Quantum Optics, Quantum Fluid Dynamics, and Quantum Field Theory, just to mention a few. We discuss the quantum mechanical setting of a system described...

Functions with small and large spectra as (non)extreme points
Speaker: Konstantin Dyakonov (ICREA & Universitat de Barcelona, Spain)
Let $\Lambda$ be a subset of $\mathbb Z_+:=\{0,1,2,\dots\}$, and let $H^\infty(\Lambda)$ denote the space of bounded analytic functions $f$ on the unit disk whose coefficients $\widehat f(k)$ vanish for $k\notin\La$. Assuming that either $\Lambda$ or $\mathbb Z_+\setminus\Lambda$ is finite,...

Monads on the category of metric spaces
Speaker: Jirí Adámek (Technische Universität Braunschweig, Germany)
The category Met of metric spaces and nonexpanding maps is locally countably presentable in the enriched sense. It follows from the work of Kelly and Power that for countably accessible monads T on Met the category of algebras can be described as an equational category of S-algebras for a...

Lax epimorphisms and the associated factorization
Speaker: Lurdes Sousa (CMUC and IP Viseu)
Lax epimorphisms (also called co-fully-faithful morphisms) are a 2-dimensional version of epimorphisms; in a 2-category A they are precisely the 1-cells f making A(f,C) fully faithful for all objects C. In this talk, several features of lax epimorphisms will be presented. We show that any...

Strain and stress-rate type viscoelastic models in the context of implicit constitutive theory

Yasemin Sengul (Cardiff University, UK)


In the constitutive equations for the classical viscoelastic models, stress tensor is expressed in terms of the strain tensor and its time derivative. However, the classical elastic and viscoelastic models are incapable of explaining the phenomena when the stress is big and the strain is...

Studying topology via ultrafilter convergence, categorically
Speaker: Maria Manuel Clementino (CMUC / Univ. Coimbra)
Inspired on the role of ultrafilter convergence in topological spaces, we will present extensions of several topological notions and results to the more general setting of monad-quantale-enriched categories....

When are epimorphisms of profinite groups surjective?
Speaker: Herman Goulet-Ouellet (PhD student, CMUC)
After a brief historical survey, we give a positive answer for full subcategories of profinite groups corresponding to Melnikov formations. We proceed to deduce that epimorphisms of pronilpotent groups are surjective. Finally, we discuss some negative examples and open problems....

Convexity and PDEs
Speaker: Julio D. Rossi (Universidad de Buenos Aires, Argentina)

An algebraic-topological approach to the classification of formal languages
Speaker: Jorge Almeida (CMUP, FCUP)
Pervasive in mathematical linguistics and computer science, (formal) languages present many interesting and difficult problems. Various mathematical theories have been developed to deal with them. Of particular importance is the classification of languages in various classes of interest,...

The AIM Conjecture
Speaker: Michael Kinyon (University of Denver, USA)
A long-standing open problem in loop theory has been to show that a loop with abelian inner mapping group is nilpotent of class at most 3. In this talk, I will describe the affirmative solution to this problem. No background in quasigroups or loops is needed, just some familiarity with what...

A new diagonal separation and its relations with the Hausdorff property
Speaker: Igor Arrieta (PhD student, CMUC)
Let P be a property of subobjects relevant in a category C. An object X in C is P-separated if the diagonal in X × X has P; thus e.g. closedness in the category of topological spaces (resp. locales) induces the Hausdorff (resp. strong Hausdorff) axiom. In this talk we consider the...

Representations of fundamental groups of surfaces
Speaker: Peter Gothen (CMUP, FCUP)
We consider representations of the fundamental group of a closed surface in the group SL(2,R). To each such representation one can associate an integer invariant called the Toledo invariant. A theorem of J. Milnor says that the absolute value of the Toledo invariant is less than or equal to...

Dynamical implications of convexity beyond dynamical convexity
Speaker: Leonardo Macarini (IST, Portugal)
We will show sharp dynamical implications of convexity on symmetric spheres that do not follow from dynamical convexity. It allows us to furnish new examples of dynamically convex contact forms that are not equivalent to convex ones via contactomorphisms that preserve the symmetry. Moreover,...

On simple 15-dimensional Lie algebras in characteristic 2
Speaker: Pasha Zusmanovich (Univ. Ostrava, Czech Republic)
Classification of finite-dimensional Lie algebras over a field of characteristic 2 is a widely open problem. We will discuss a certain 15-dimensional such algebra, first appearing in the works of Skryabin. It possesses a number of interesting properties which may be typical for a certain...

Entropy-Transport distances between measures and metric measure spaces
Speaker: Nicolò De Ponti (SISSA, Trieste, Italy)
See the attached file ...

A glance at Poisson manifolds, Courant algebroids and Lie-infinity algebras
Speaker: Joana Nunes da Costa (CMUC, Univ. Coimbra)
The goal of the talk is to give an overview of some aspects of Poisson geometry. I will start with the definition of Poisson manifold, then I will introduce Courant algebroids. Finally, I will present recent topics where I've been working on, related to Courant algebroids and Lie-infinity...

3-manifolds, knots and surfaces
Speaker: João Nogueira (CMUC, Univ. Coimbra)
We will survey the motivation and history of 3-manifold topology, together with its twin subject of knot theory, giving emphasis to the importance of surfaces and groups on the understanding of these subjects. Under this framework, we will review some recent developments and guiding...

The regularity of Eulerian ideals
Speaker: Jorge Sentieiro Neves (CMUC, Univ. Coimbra)
The Eulerian ideal of a graph establishes yet another bridge between algebra and combinatorics. It encodes much information about the graph: its generators can be related to the Eulerian subgraphs with an even number of edges and, for a fixed monomial order, the associated standard...

Relaxed solutions for incompressible inviscid flows: A variational and gravitational approximation to the initial value problem
Speaker: Ivan Moyano (University of Nice Sophia Antipolis, France)
Following Arnold's geometric interpretation, the Euler equations of an incompressible fluid moving in a domain D are known to be the optimality equation of the minimizing geodesic problem along the group of orientation and volume preserving diffeomorphisms of D. This problem admits a...

Enriched functional limit theorems for chaotic dynamics and heavy tailed observables
Speaker: Jorge Freitas (CMUP, FCUP)
We consider stochastic processes arising from chaotic systems by evaluating an heavy tailed observable function along the orbits of the system. We prove the convergence of a normalised sum process to a Lévy process with excursions, designed to describe the oscillations observed during...

Families of polytopes with rational linear precision in higher dimensions
Speaker: Eliana Duarte (CMUP, Univ. Porto)
Polytopes with rational linear precision are of interest in the Geometric Modeling community because of their approximation properties and it is an open question to classify them in dimension d > 2. This classification question is closely related to discrete statistical models with...

Monoid extensions and the Grothendieck construction
Speaker: Graham Manuell (CMUC)
It is well known to category theorists that the Schreier theory of group extensions can be understood in terms of the Grothendieck construction on indexed categories, but the case of monoid extensions is seldom mentioned. In this talk I will describe how the classification of Schreier and...

Submonads of the presheaf monad and their algebras
Speaker: Carlos Fitas (PhD student, CMUC)
After recalling a few fundamental notions about V-Cat, V-Rel and V-Dist, where V is a quantale, we will present two new characterizations of the submonads of the presheaf monad: one in terms of a special class of V-distributors; and another as those monads which are fully (BC)*, lax...

Why I like noncommutative algebra: a tour of symmetry, geometry and mathematical physics
Speaker: Samuel Lopes (CMUP, FCUP)
I will start by motivating the study of noncommutative algebra and representation theory through examples rooted in symmetry, geometry and mathematical physics. Then I will talk about more specific aspects of my research interests....

Quinn Finite Total Homotopy TQFT as a once-extended TQFT
Speaker: João Faria Martins (Univ. Leeds, UK) 
Quinn Finite Total Homotopy TQFT is a TQFT that works in any dimension and that depends on the choice of a homotopy finite space $B$ (e.g. $B$ can be the classifying space of a finite group or of a finite 2-group). I will report on ongoing joint work with Tim Porter on once-extended versions...

On the lattice of restricted subalgebras of a restricted Lie algebra
Speaker: Pilar Paez-Guillán (Univ. Santiago de Compostela, Spain)
Historically, the question of how far the properties of the subgroup lattice of a group G determine those of G has been extensively studied. Similar questions have been formulated for Lie algebras and restricted Lie algebras.In this talk, we will give a general characterization for...

From Krohn-Rhodes theory to Markov chains
Speaker: Pedro Silva (CMUP, FCUP)
In the early sixties, Krohn-Rhodes theory became a cornerstone of both finite semigroup theory and automata theory. The theory expanded subsequently in different directions, including the infinite setting and applications to the theory of Markov chains. The results mentioned are joint work...

Algebraic geometry with computer algebra
Speaker: Carlos Rito (CMUP)
The goal of the talk is to highlight the usefulness of modern computer algebra tools in the study of more classic algebraic geometry problems. I will give some examples related to my research on Schoen surfaces, Godeaux surfaces and the canonical map of surfaces of general type....

A non-variational approach for the porous medium equation
Speaker: Makson Santos (USP, São Carlos, Brazil)

On the ternary commutator I: Exact Mal'tsev categories
Speaker: Cyrille Sandry Simeu (UCLouvain, Belgium)
Please, find the abstract attached....

An orthogonal approach to algebraic weak factorisation systems
Speaker: John Bourke (Masaryk Univ., Czech Republic)
Factorisation systems (both weak and strong) are commonly defined as consisting of two classes of maps satisfying a certain orthogonality relation and a factorisation axiom. The standard definition of algebraic weak factorisation system, involving comonads and monads, is rather different. ...

Orthogonal symmetric matrices and joins of graphs
Speaker: Helena Smigoc (Univ. College Dublin, Ireland)
We ask when is the join of two (possibly disconnected) graphs G and H the pattern of an orthogonal symmetric matrix. A notion of compatibility for multiplicity matrices gives rise to a necessary condition. To address sufficiency, we introduce generic realisability that generalises the...

Point-free measures: a localic approach to measure theory
Speaker: Raquel Bernardes (PhD student, CMUC)
Motivated by the fact that σ-locales generalize measurable spaces and seeking to overcome some restrictions of measure theory, Alex Simpson [1] proposed an approach to measure theory in the framework of point-free topology. This talk will be a general survey of that approach while...

Effective descent in internal multicategories
Speaker: Rui Prezado (PhD student, CMUC)
The Bénabou-Roubaud theorem [BR70] and Beck's monadicity theorem allow us to characterize effective descent morphisms in locally cartesian closed categories; these are exactly the pullback-stable regular epimorphisms. However, characterization of effective descent morphisms is far...

Esakia duality and its connection with pointfree Pervin spaces
Speaker: Anna Laura Suarez (Université Côte d'Azur, France)
Frames are complete Heyting algebras, but frame maps need not preserve the Heyting arrow. Those maps that preserve it are called open maps. Using the classical adjunction between frames and spaces, one can show that frames with open maps are dual to topological spaces with maps satisfying a...

Deciding implications of matrix properties
Speaker: Michael Hoefnagel (Stellenbosch Univ., South Africa)
Matrix properties were first introduced by Z. Janelidze in 2006, as a class of exactness properties that may be represented by (extended) matrices of terms in an algebraic theory. In the simplest case, i.e., when the given algebraic theory is the algebraic theory of sets, matrix properties...

Lax factorisation systems and categories of partial maps
Speaker: Leonardo Larizza (PhD student, CMUC)
Factorisation systems describe morphisms in a category by factorising them into pairs of composable morphisms. Their definition depends on an orthogonality relation between morphisms, which entails the existence of some diagonal morphisms for certain squares. In this seminar we present the...

Split extensions of bialgebras
Speaker: Florence Sterck (UCLouvain, Louvain-la-Neuve)
In the category of groups, split extensions have a lot of interesting properties. One of them is the fact that the category of split extensions is equivalent to the category of group actions. Unfortunately, this does not hold in any category, for example the category of monoids does not have...

Elliptic regularity for some degenerate equations
Speaker: Héctor A. Chang-Lara (CIMAT, Mexico)

Preordered actions of preordered monoids
Speaker: Manuela Sobral (CMUC, Univ. Coimbra)
Definitions and results on preordered monoids and Schreier split epimorphisms of monoids will be recalled in order to replicate the equivalence between Schreier split extensions of monoids and monoid actions in an appropriate subcategory of the category of preordered monoids....

Continuity of localic maps and localization morphisms
Speaker: Jorge Picado (CMUC, Univ. Coimbra)
By definition, a map between topological spaces is continuous if preimages of open sets are open or, equivalently, preimages of closed sets are closed. Can one get similar characterizations for localic maps between locales? The characterization of localic maps in terms related to continuity...

Eulerian polynomials via the Weyl algebra action
Speaker: José Agapito Ruiz (Univ. Lisboa)
We obtain a generalization of the Worpitzky identity and new recursive formulas for a family of polynomials that include the classical Eulerian polynomials, using the action of the Weyl algebra on the geometric series and the framework of rook placements on Ferrers boards for combinatorial...

Regularity for \(C^{1,\alpha}\) interface transmission problems
Speaker: María Soria-Carro (UT Austin, USA)

Polynomial identities and central polynomials: their growth
Speaker: Carla Rizzo (Univ. Palermo, Italy)
A central polynomial of an algebra A is a polynomial f in non-commutative variables that takes central values when evaluated in A. In case it vanishes in A, f is called a polynomial identity of A, otherwise f is a proper central polynomial of A. The purpose of this talk is to survey some old...

Symplectic left and right keys - Type C Willis' direct way
Speaker: João Miguel Santos (PhD student, CMUC)
The right and left key maps for Kashiwara-Nakashima tableaux are used to describe type C Demazure and opposite Demazure crystals, respectively. For instance, Fu-Lascoux non-symmetric Cauchy kernels expand into products of opposite Demazure characters and Demazure atoms. These key maps are...

The category of Frith frames
Speaker: Célia Borlido (CMUC, Univ. Coimbra)
A Frith frame is a frame equipped with a join-dense bounded sublattice. In this talk we will see that Frith frames and suitable morphisms form a category Frith which is equivalent to the category of transitive and totally bounded quasi-uniform frames. This equivalence provides a very simple...

Generalized quantale-enriched categories: a digression
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
This is an informal digression through the study, of the last two decades, of (generalized) quantale-enriched categories, aiming to present both results and remaining open problems on exponentiability and descent theory....

The optimal transport problem: regularity (and existence)
Speaker: Yash Jhaveri (Columbia University, USA)

The first cohomology object in semi-abelian categories
Speaker: James Gray (Stellenbosch Univ., South Africa)
We show that there is a natural notion of internal crossed homomorphism object of a split extension, defined as the representing object of a certain functor. Using these objects one can construct the first internal cohomology object of a split extension. We show that although these objects...

The reflexive completion in context
Speaker: Tom Leinster (University of Edinburgh, Scotland)
For a small category A, Isbell conjugacy defines an adjunction between the functor categories [A^op, Set] and [A, Set]^op. The invariant part of this adjunction (that is, its category of fixed points) is called the reflexive completion of A.I will describe some results relating the reflexive...

Generalizations of the Fourier transform and their applications
Speaker: Rita Guerra (CMUC)
In this talk, we consider a new generalization of the Fourier transform, depending on four complex parameters and all the powers of the Fourier transform. This new transform is studied in some Lebesgue spaces. We begin with the characterization of each operator by its characteristic...

Torsion pairs and Ringel duality for Schur algebras
Speaker: Karin Erdmann (Univ. of Oxford, UK)
A finite-dimensional quasi-hereditary algebra  has a Ringel dual which is again quasi-hereditary. For blocks of  both the classical and quantum Schur algebras S(2,r) and Sq(2,r) we show they are Morita equivalent to their Ringel duals if they contain 2pk simple modules. This uses a...

Categorical aspects of the non-abelian tensor product
Speaker: Tim Van der Linden (UCLouvain, Belgium)
We give an overview of joint work with Davide di Micco on an approach to the Brown-Loday non-abelian tensor product in the context of semi-abelian categories. We discuss the link with (internal) crossed squares and pairs of compatible actions, and present some examples and applications....

Congruence modular variety and algebraic crystallography
Speaker: Dominique Bourn (Université du Littoral, Calais, France)
See the attached file....

Uniform locales and their constructive aspects
Speaker: Graham Manuell (CMUC)
Much work has been done on porting the theory of uniform spaces to the pointfree context and uniform frames/locales have proved to be a useful tool in this setting. However, much of the utility of the pointfree approach lies in its constructive theory. Formulating topological results...

A new diagonal separation and its relations with the Hausdorff property
Speaker: Igor Arrieta (CMUC)
Let P be a property of subobjects relevant in a category C. An object X in C is P-separated if the diagonal in X × X has P; thus e.g. closedness in the category of topological spaces (resp. locales) induces the Hausdorff (resp. strong Hausdorff) axiom.In this talk we consider the...

A uniform action of the dihedral group \(\mathbb{Z}_2 \times D_3\) on Littlewood-Richardson coefficients
Speaker: Olga Azenhas (CMUC, Univ. Coimbra)
The Littlewood-Richardson (LR) coefficient symmetries under the action of the dihedral group \( \mathbb Z_2\times D_3 \) of order twelve refers to the invariance of LR coefficients, under an action of that group on LR triples of partitions, the partition-triples indexing LR...

Smooth representations of groups associated with algebras defined over non-archimedean fields
Speaker: João Dias (CEAFEL, Univ. Lisboa)
In this talk, I will show a description of the irreducible smooth representations of algebra groups, unit groups of a split basic algebra and involutive algebra groups over a non-archimedean field (for example the p-adic field). In particular, I will discuss the admissibility and...

Bounded weak solutions to elliptic PDE with data in Orlicz spaces
Speaker: David Cruz-Uribe (Univ. Alabama, USA)
See the attached file...

Feedback control of falling liquid films using a hierarchical model approach

Susana Gomes (Univ. Warwick, UK)

The flow of a thin film down an inclined plane is a canonical setup in fluid mechanics and associated technologies, with applications such as coating, where the liquid-gas interface should ideally be flat, and heat or mass transfer, where an increase of interfacial area is desirable. In each...

Context-free word problem semigroups
Speaker: Tara Brough (NOVA Univ. of Lisbon)
Please, see the attached file....

Algebraically cocomplete categories
Speaker: Jiri Adámek (Technische Universität Braunschweig, Germany)
Dualizing the concept introduced by Freyd in 1990, a category is called algebraically cocomplete if every endofunctor has a terminal coalgebra. Among cocomplete categories these are just preordered classes. However, assuming the generalized continuum hypothesis (GCH), we present nice...

Jones polynomial, Khovanov homology and its geometrization
Speaker: Marithania Silvero (Univ. Seville, Spain)
Knot Theory studies the classification of knots and links. Jones polynomial, introduced by Vaughan Jones in 1984, was one of the greatest breakthrough in this area, since it was the first polynomial knot invariant allowing to distinguish a knot from its mirror image. At the end of the past...

Entropy dissipation via Information Gamma calculus
Speaker: Wuchen Li (Univ. South Carolina, USA)
In this talk, we present the convergence behavior for some non-gradient degenerate stochastic differential equations towards their invariant distributions in this talk. Our method extends the connection between Gamma calculus and Hessian operators in the L^2-Wasserstein space. In detail, we...

Minimal sets of generators
Speaker: Alberto Facchini (Università di Padova, Italy)
A minimal set of generators of a right module MR over an associative ring R with identity is a subset X of M that generates M, but for any x∈ X, X∖{x} generates a proper submodule of MR. Unlike in the case of R a division ring, minimal sets of generators have little to do with...

Zariski-type spectra of localic ring-like structures
Speaker: Graham Manuell (CMUC, Univ. Coimbra)
The Zariski spectrum provides a way to associate a locale to a commutative ring. Other spectrum constructions include the Stone spectrum of a distributive lattice and the prime spectrum of an MV-algebra. In many cases the algebraic structure comes equipped with a topology which must be taken...

Peg Problems
Speaker: Joshua Greene (Boston College, USA)
Toeplitz asked in 1911 whether any Jordan curve in the Euclidean plane contains the vertices of a square. The problem remains open, but it has given rise to many interesting variations and partial results. I will discuss the proof of a related result which is best possible when the curve...

Besov-Morrey and Triebel-Lizorkin-Morrey spaces with variable exponents
Speaker: António Caetano (Univ. Aveiro)
Our aim in this talk is to consider Besov-Morrey and Triebel-Lizorkin-Morrey spaces with variable exponents and present some of their properties, in particular the atomic and molecular representations. This reports on joint work with Alexandre Almeida (Besov-Morrey spaces) and Henning Kempka...

Speaker: Walter Tholen (York Univ., Toronto, Canada)
Extending Guitart's work of the 1970s, in this talk we eventually present the formation of the diagram category of a category and the formation of the Grothendieck category of a CAT-valued functor as adjoint 2-functors, and then establish a considerable generalization thereof. This...

Partial evaluations for monads and 2-monads
Speaker: Paolo Perrone (University of Oxford, UK)
Partial evaluations are a way to encode, in terms of monads, operations which have been computed only partially. For example, the sum "1+2+3+4" can be evaluated to "10", but also partially evaluated to "3+7", or to "6+4".Such structures can be defined...

The deformation cohomology of a symplectic groupoid
Speaker: João Nuno Mestre (CMUC, Univ. Coimbra)
Symplectic groupoids are geometric objects that function as global counterparts to Poisson manifolds, in the same way that Lie groups are global counterparts to Lie algebras.In this talk I will first give an idea of how that analogy works, and I will present the construction of the...

Stochastic optimization of multiple objectives and fairness in machine learning
Speaker: Luís Nunes Vicente (Lehigh Univ., USA & CMUC, Univ. Coimbra)
In the application of machine learning to real life decision-making systems, e.g., credit scoring and criminal justice, the prediction outcomes might discriminate against people with sensitive attributes, leading to unfairness. The commonly used strategy in fair machine learning is to...

Wallach spaces and Dirac operators
Speaker: Ana Cristina Ferreira (CMAT, Univ. Minho)
Generalized Wallach spaces are homogeneous spaces of type III, sometimes also called tri-symmetric spaces in the literature. The 'original' Wallach spaces are those of positive sectional curvature and there exist only three of them in dimensions 6, 12 and 24. The three cases are related to...

On the 3x3x3-Lemma
Speaker: Tim Van der Linden (UCLouvain, Belgium)
The idea of a short exact sequence of short exact sequences naturally leads to the 3x3-Lemma. What happens when this process is repeated? The aim of this talk is to explain the connection between the concept of a 3-fold extension, short exact sequences of 3x3-diagrams, and a congruence...

Abstract and concrete spectral spaces
Speaker: George Janelidze (Univ. Cape Town, South Africa)
In this joint work with Alberto Facchini and Carmelo Antonio Finocchiaro we begin with a complete lattice L equipped with a binary multiplication such that the product of any two elements is less or equal to their meet. As suggested by the so-called "Abstract ideal theory" we...

Symbolic data and optimization

Paula Amaral (NOVA Univ. of Lisbon)

Today, in many areas, we collect huge volumes of data to analyse. To use this data in classification methods it is necessary to aggregate them keeping as much information as possible about the data. Histograms are a useful way of representing large sets of data keeping...

Why I like noncommutative algebra: A tour of symmetry, geometry and mathematical physics
Speaker: Samuel Lopes (CMUP, Univ. Porto)
I will start by motivating the study or noncommutative algebra and representation theory through examples rooted in symmetry, geometry and mathematical physics. Then I will talk about more specific aspects of my research interests....

Shifted Bender-Knuth moves and a shifted Berenstein-Kirillov group
Speaker: Inês Rodrigues (CEAFEL, Univ. Lisboa)
The Bender-Knuth moves on Young tableaux are well-known involutions, namely, they are used in a combinatorial proof that the Schur functions are symmetric, as well as in alternative proofs of the classic Littlewood-Richardson rule. The group generated by these involutions, modulo the...

A new algorithm for the multiobjective minimum spanning tree
Speaker: José Luís Santos (CMUC, Univ. Coimbra)
In this talk a new algorithm for the multiobjective minimum spanning tree problem is presented. It is based on a label algorithm for the multiobjective shortest path problem in a transformed network and can be used with any number of criteria. Some...

A new approach to S-protomodular categories
Speaker: Tamar Janelidze-Gray (Univ. Cape Town, South Africa)
We propose a new approach to S-protomodular categories in the sense of D. Bourn, N. Martins-Ferreira, A. Montoli, and M. Sobral. Instead of points (=split epimorphisms) it uses generalized points, which we define as composable pairs of morphisms whose composites are pullback stable regular...

Relaxed actions of monoids: Towards a new cohomology theory
Speaker: Peter Faul (University of Cambridge, UK)
Artin glueings between frames have much in common with semidirect products of groups. If H and N are groups (frames) then the process of constructing semidirect products (Artin glueings) provides a means of finding all objects in which N embeds as a normal (closed) subobject and H embeds as...

The s-numbers, eigenvalues and generalized trigonometric functions
Speaker: Jan Lang (Ohio State Univ., USA)
Generalized trigonometric functions, which were first introduced by Lundberg 1879, will be discussed together with their connections with p-Laplacian, approximation theory and s-numbers for Sobolev embedding. ...

Sharp inequalities for the Ornstein-Uhlenbeck operator
Speaker: Lubos Pick (Charles Univ., Prague, Czechia)
The abstract is attached....

Model-based evaluation of school- and non-school based public health measures on controlling the COVID-19 pandemic in the Netherlands
Speaker: Ganna Rozhnova (University Medical Center Utrecht, Netherlands)
Introduction: In autumn 2020, many countries, including the Netherlands, are experiencing a second wave of the COVID-19 pandemic. Health policymakers are struggling with choosing the right mix of measures to keep the COVID-19 case numbers under control, but still allow a minimum of social...

Commutation classes of the reduced words for the longest element of the symmetric group
Speaker: Ricardo Mamede (CMUC, Univ. Coimbra)
Using the standard Coxeter presentation for the symmetric group, two reduced expressions for the same group element w are said to be commutationally equivalent if one expression can be obtained from the other one  by applying a finite sequence of commutations. The commutation...

Quasihereditary algebras with exact Borel subalgebras
Speaker: Teresa Conde (Univ. Stuttgart, Germany)
Exact Borel subalgebras of quasihereditary algebras emulate the role of "classic" Borel subalgebras of complex semisimple Lie algebras. Not every quasihereditary algebra A has an exact Borel subalgebra. However, a theorem by Koenig, Külshammer and Ovsienko establishes that...

Characterizations of normality given by \(C\)-, \(C^*\)- and \(z\)-embedded sublocales
Speaker: Ana Belén Avilez (PhD student, CMUC)
Please, see the attached file....

Sublocales as parts
Speaker: Imanol Mozo Carollo (Univ. of the Basque Country, Bilbao, Spain)
Please, find the attached file....

Laws of rare events for chaotic dynamics
Speaker: Ana Cristina Moreira de Freitas (CMUP, Univ. Porto)
The extremal index appears as a parameter in Extreme Value Laws, characterising the clustering of extreme events. We apply this idea to a dynamical systems context to analyse the possible extreme value laws for the stochastic process generated by observations taken along dynamical orbits....

Strong solutions of parabolic equations with \(p(x,t)\)-Laplacian: existence and the global regularity properties
Speaker: Sergey Shmarev (Univ. Oviedo, Spain)

The Schroedinger problem
Speaker: Dmitry Vorotnikov (CMUC, Univ. Coimbra)
Schroedinger’s hot gas experiment aimed for determining the most likely evolution between two subsequent observations of a cloud of particles. Seemingly purely stochastic, this problem can be translated into a geometric language. Given a fixed functional on a Riemannian...

Complex network of epidemic models

Cristiana J. Silva (CIDMA, Univ. Aveiro)

In this work, we consider an epidemiological model given by a system of ordinary equations, for the transmission dynamics of SARS-CoV-2, with piecewise constant parameters. Based on this model, we construct a complex network of dynamical systems, in order to take into account the...

Statistical stability in chaotic systems (CANCELLED)

José Ferreira Alves (CMUP, Univ. Porto)

We will make a brief introduction to the theory of dynamical systems, focusing our attention on the class of chaotic systems. We will pay special attention to the Lorenz attractor, well known for the "butterfly effect". We will see that, despite the impossibility of predicting...

On the combinatorics of linear dependencies of 0-1 vectors
Speaker: Ilda Perez Fernandez Silva (Univ. Lisboa)
It was recently proven (J. Geelen, B. Gerards, G. Whittle) that linear dependence over any given finite field can be characterized combinatorically, via matroids, in terms of a finite number of excluded subconfigurations (minors). It is known that representability over the reals can not be...

Link invariants from finite crossed modules and a lifting of the Eisermann invariant
Speaker: Roger Picken (IST, Univ. Lisbon)
This talk is based on work with João Faria Martins (Univ. Leeds) [1] and several projects with students. I will describe the construction of an invariant of tangles and framed tangles which takes values in an arbitrary crossed module of finite groups. This involves the fundamental...

Training reaction diffusion models for image restoration
Speaker: Sílvia Barbeiro (CMUC, Univ. Coimbra)
Image restoration is one of the major concerns in image processing with many interesting applications. In the last decades there has been intensive research around the topic and hence new approaches are constantly emerging. Partial differential equation (PDE) based models, namely of...

Finite fields meet Markov chains
Speaker: Persi Diaconis (Stanford Univ., USA)
In joint work with Jimmy He and Marty Isaacs we have been exploring a curious interface between Galois theory and Probability. The problems are easy to state: Consider first Z/pZ. A random walk takes x to x+1 or x-1 with probability 1/2. As I will explain, it takes order p^2 steps (N&S)...

Characterization of coextensive varieties of universal algebras
Speaker: David Neal Broodryk (University of Cape Town, South Africa)
A coextensive category can be defined as a category C with finite products such that for each pair X,Y of objects in C, the canonical functor ×:X/C×Y/C→(X×Y)/C is an equivalence. This is the dual of an extensive category, a term that was first used by W. F. Lawvere and...

Pretorsion theories and internal preorders
Speaker: Marino Gran (UCLouvain, Belgium)
Please, find the attached file....

Mathematical modelling in solid mechanics: an example with fracking
Speaker: Nicolas Van Goethem (CMAFCIO, Univ. Lisboa)
I will present the various steps of mathematical modelling on a practical case: presentation and setting of the problem (hydraulic fracture), choice of the approach (energergetical and variational), choice of the method (topological differentiation), design of the algorithm (quasi-static and...

Fully nonlinear dead-core systems
Speaker: Rafayel Teymurazyan (CMUC)
We study fully nonlinear dead-core systems coupled with strong absorption terms. We discover a chain reaction, exploiting properties of an equation along the system. The lack of both the classical Perron's method and comparison principle for the systems requires new tools for tackling the...

Unfolding a Bykov attractor: from an attracting torus to strange attractors
Speaker: Alexandre Rodrigues (CMUP, Univ. Porto)
We present a comprehensive mechanism for the emergence of strange attractors in a two-parametric family of differential equations acting on a three-dimensional sphere. When both parameters are zero, its flow exhibits an attracting heteroclinic network (Bykov network) made by two...

Geometry and Topology of Higgs bundles moduli spaces
Speaker: André Oliveira (CMUP, Univ. Porto)
A Higgs bundle over a Riemann surface is a pair consisting of a vector bundle together with some extra data. Their moduli spaces are quasi-projective varieties which naturally appear in many different areas of Mathematics and even of Physics. In this talk, we will take a general overview...

An introduction to combinatorial commutative algebra
Speaker: Jorge Neves (CMUC, Univ. Coimbra)
Combinatorial Commutative Algebra comes of age following the works of Richard Stanley in the late seventies of the last century. A typical research problem consists of associating an ideal (or ring) to a given type of structure (simplicial complexes, graphs, polytopes, matroids, etc.) and to...

On orthogonal polynomials and their applications
Speaker: José Carlos Petronilho (CMUC, University of Coimbra)
In this talk we will give an overview of the theory of orthogonal polynomials (OP), focusing on the so-called inverse problems. The problems to be considered arise in the framework of Sobolev OP and the theory of polynomial mappings. We will point out several applications, including...

The theory of exactness properties: recent developments and work in progress
Speaker: Zurab Janelidze (Stellenbosch University, South Africa)
By the "theory of exactness properties" we mean a subject that is in similar relation to the theories of semi-abelian categories, abelian categories, etc., as universal algebra is to group theory, module theory, etc. These classes of categories (semi-abelian, abelian, etc.) are...

Variations on distributive laws
Speaker: Nicola Gambino (University of Leeds, UK)
The notion of a distributive law between monads goes back to fundamental work of Jon Beck from the late ‘60s. Just as a monad describes a kind of algebraic structure, a distributive law between two monads describes how the algebraic structure for one monad distributes over the...

Mathematical models and methods for Breach Formation in Earth Embankment Dams
Speaker: Giuseppe Romanazzi (Unicamp, Campinas, Brazil)
After an overview of breach formation in embankment dams, we present different mathematical models and methods used nowadays to predict the formation of breach in earth embankments. The strengths and weaknesses of the prediction models are discussed....

The Karoubi envelope of the mirage of a subshift
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
Free profinite semigroups are completions of free semigroups, and for that reason their elements are frequently called pseudowords. Around 2003, Almeida introduced a fruitful connection between symbolic dynamical systems (also known as subshifts) and free profinite semigroups. Following...

The polycyclic inverse monoids and the Thompson groups revisited
Speaker: Mark Lawson (Heriot-Watt University, UK)
Please, see the attached file....

Discrete covers of locales
Speaker: Igor Arrieta Torres (PhD Student, CMUC)
See attached file....

Some fibrational properties of normal monomorphisms
Speaker: Giuseppe Metere (Universitá degli Studi di Palermo, Italy)
Several classes of monomorphisms have been introduced in general algebraic contexts. For some of them, there is a purely categorical description that makes it possible a formal study of their structure. In my talk, after a quick recap of such notions, I will focus on the normal subobjects in...

Cactus group actions on shifted tableau crystals and a shifted Berenstein-Kirillov group
Speaker: Inês Rodrigues (CEAFEL, Univ. Lisboa)
Recently, Gillespie, Levinson and Purbhoo introduced a crystal-like structure for shifted tableaux, called the shifted tableau crystal. We introduce a shifted version of the crystal reflection operators, which coincide with the restrictions of the shifted Schützenberger involution to...

Tensors of KZ-algebras
Speaker: Marcelo Fiore (University of Cambridge, UK)
We investigate tensors of pseudo-algebras for KZ (aka lax idempotent) 2-monads. Our leading example is the tensor product of (unsorted) algebraic theories. This will be used throughout the talk to motivate and present the abstract theory.We shall consider tensors both in the sense of...

Characterizations of lax orthogonal factorization systems
Speaker: Charles Walker (Masaryk University, Czech Republic)
See attached file....

Intrinsic Schreier split extensions and intrinsic Schreier special objects
Speaker: Andrea Montoli (Univ. degli Studi di Milano, Italy)
We explore, in the context of regular unital categories with comonadic projective covers, intrinsic notions of Schreier split epimorphisms and Schreier special objects. These intrinsic notions allow, on one hand, to understand categorically the properties of Schreier split extensions of...

Double categories of open dynamical systems
Speaker: David Jaz Myers (Johns Hopkins University, USA)
A dynamical system consists of a notion of how things may be, and a notion of how things may change, given how they are. There are many sorts of dynamical systems --- discrete, continuous, probabilistic, non-deterministic --- and the dynamics often depend on parameters which themselves may...

A non-Levi branching rule in terms of Littelmann paths
Speaker: Jacinta Perez Gavilan Torres (Institute of Mathematics, Polish Academy of Sciences)
We will give an introduction to the Littelmann path model for representations of simple Lie algebras, highlighting its most important applications and connectionsto algebraic combinatorics. Then we will present a non-Levi branching rule in terms of Littelmann paths. This is joint work with...

From preordered groups to quantale-enriched groups
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
Based on the study of preordered groups of [1], we introduce and study V-groups and their homomorphisms, for a commutative and unital quantale V.(This talk is based on joint work with Andrea Montoli [2].) References:[1] M.M. Clementino, N. Martins-Ferreira, A. Montoli, On the...

Actions of preordered monoids and their associated extensions
Speaker: Nelson Martins-Ferreira (IP Leiria, CDRSP)
The category of preordered monoids can be seen either as a category of internal preorders in monoids or as the category of internal monoids in preorders. In this talk, we start by analysing differences and similarities between preordered groups and preordered monoids. In particular, we study...

Sharp concentration estimates near criticality for sign-changing solutions of Dirichlet and Neumann problems
Speaker: Hugo Tavares (IST, Univ. Lisboa)
Consider the slightly subcritical problem $-\Delta u_\varepsilon = |u_\varepsilon|^{\frac{4}{n-2}-\varepsilon}u_\varepsilon$ either on $\mathbb{R}^n$ ($n\geq 3$) or in a ball $B$ satisfying Dirichlet or Neumann boundary conditions. For radial solutions, we provide sharp rates and constants...

Is fractional calculus the ultimate solution to all anomalous-diffusion problems?
Speaker: Luís Ferrás (Univ. do Minho)
Albert Einstein, in his work regarding Brownian motion (1905) entitled "On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat", gave the definitive confirmation that atoms and molecules exist. Since then, many works have...

Revisiting the relation between subspaces and sublocales
Speaker: Anna Laura Suarez (Univ. Birmingham, UK)
One of the main features distinguishing pointfree topology from classical point-set one is that in the pointfree setting a space (i.e. a locale) may have abstract subspaces (sublocales) which do not have any point-set analogue. The lattice of sublocales of a locale will not in general be a...

Enriched Priestley spaces
Speaker: Dirk Hofmann (Univ. Aveiro)
See attached file....

Optimization meets Medical Physics: tailored algorithms
Speaker: Humberto Rocha (School of Economics, Univ. Coimbra)
Radiotherapy has been a fertile field for the development of algorithms to tackle the different optimization problems that arise in this area. A panoply of algorithms has been used for different problems including integer programming, linear programming or quadratic programming algorithms....

Sweeping processes and evolution problems with bounded variation
Speaker: Manuel Monteiro Marques (Univ. Lisboa)
Evolution problems governed by maximal monotone operators with domains that depend on time are present in many areas.The special case of the sweeping process, where the operators are normal cones to time-dependent convex moving sets, was treated by Jean Jacques Moreau in the seventies,...

On q-polynomials: some old and new results
Speaker: Renato Álvarez-Nodarse (Univ. Sevilla, Spain)
The first family of q-polynomials appears in the works of Stieltjes and at the end of the XIX century, and have been attracted great interest since then. They are related with a lot of pure mathematical problems but also with applied ones. In this talk I will try to give an idea of the...

On difunctionality of class relations
Speaker: Diana Rodelo (CMUC and Univ. Algarve)
See attached file....

Categorical aspects of congruence distributivity
Speaker: Idriss Tchoffo Nguefeu (UCLouvain, Belgium)
We give new characterisations of regular Mal'tsev categories with distributive lattice of equivalence relations through variations of the so-called Triangular Lemma and Trapezoid Lemma in universal algebra. We then give new characterisations of equivalence distributive Goursat categories...

Mirror symmetry on the Hitchin system
Speaker: Emilio Franco Gomez (CAMGSD, IST, Lisboa)
We will provide an overview of Mirror Symmetry phenomena occurring in the framework of the Hitchin system....

Branes on the Hitchin system via torsion bundles
Speaker: André Oliveira (CMUP & UTAD)
We study the fixed point loci on the moduli space M of GL(n,C)-Higgs bundles (over a curve) for the action of tensorization by a torsion line bundle of order n. This is a hyperholomorphic loci which can be equipped with a hyperholomorphic sheaf, hence is constitutes a BBB-brane on M. Such a...

The feasible region for consecutive occurrences of large permutations
Speaker: Raúl Penaguião (Univ. Zürich, Switzerland)
The study of patterns in permutations has steadily gathered interest in combinatorics. The notion of classical pattern has been well studied so far, for instance giving rise to the limit object of a permuton. The proportions of these patterns takes values between zero and one and the precise...

Proposition 15 in Euclid's Optics
Speaker: Daniel M. Pinto (CMUC, Univ. Coimbra)
One of the oldest and, despite its flaws, most important books in geometric optics is, undoubtely, Euclid's Optics. We will take a close look at some versions and translations of the original book, paying special attention to the proof of Proposition 15....

Combinatorics and moduli of line bundles on stable curves
Speaker: Ana Margarida Melo (CMUC, Univ. Coimbra)
The moduli space of line bundles on smooth curves of given genus, the so called universal Jacobian, has a number of different compactifications over the moduli space of stable curves. These compactificatons have very interesting combinatorial properties, which can be used to describe their...

The Method of Fundamental Solutions and its application for solving shape optimization problems
Speaker: Pedro Antunes (Univ. Aberta, Lisboa)
This talk is divided into two parts. In the first part we give an overview of the application of the Method of Fundamental Solutions (MFS) for solving boundary value problems with elliptic PDE's. The MFS is a meshfree method where the solution is approximated by a linear combination of...

A walk from D-modules to distribution theory through the conjugation functor
Speaker: Teresa Monteiro Fernandes (CMAFcIO, Univ. Lisboa)
I will recall Kashiwara's conjugation functor from the derived category of regular holonomic D-modules over a complex manifold to the derived category of regular holonomic D-modules on the complex conjugate manifold \bar{X}, which he proved to be an equivalence of categories thanks to the...

Quantum matrix algebras: a review
Speaker: Dmitry Gurevich (Valenciennes Univ., France)
I plan to define certain well-known and new quantum matrix algebras (for instance, Generalized Yangians) and discuss their properties.In particular, I'll consider the problem of defining quantum determinants and other symmetric polynomials in all of them. Also, I'll exhibit some...

Information in additional observations from a non-parametric experiment
Speaker: Tilo Wiklund (Univ. of Uppsala, Sweden)
Given some statistical experiment E we may, at least in principle, make multiple, independent, repetitions of it. Say that one statistician repeats the experiment n times, while another repeats it n+1 times. How much better off will the latter be? They certainly should not do be any worse...

Specht modules for general diagrams, their Schur functions, and Mondrian tableaux
Speaker: Olga Azenhas (CMUC, Univ. Coimbra)
The question of how to decompose a Specht module, for an arbitary diagram, into irreducible submodules, is not yet known. Similar question for Schur functions for arbitrary diagrams. We discuss known results for skew shapes, in particular, border strips, or forests, and the role of R. Liu's...

Finitely presentable algebras for finitary monads
Speaker: Lurdes Sousa (CMUC and IP Viseu)
A variety of algebras is nothing else than the category of algebras of a finitary monad on Set, and, in this case, an algebra A is finitely presentable if it can be presented by a finite set of generators and a finite set of equations. We generalize this to finitary regular monads on...

Matrix functions: applications, computation and topics of research
Speaker: João Cardoso (ISEC & CMUC)
The first known references to matrix functions can be found in the works of Cayley, Laguerre, Peano and Sylvester in the second half of the 19th century.  However, just in the last decades of the 20th century we assisted to a growing interest in developing methods for the computation of...

Maths for crime prediction
Speaker: Adérito Araújo (CMUC, Univ. Coimbra)
It is undeniable that an unfortunate aspect of modern life, technologically and economically more developed, is the presence of crime distributed in major urban areas. This does not only affect countries like Portugal or the European continent, but is experienced in all countries around the...

Multiobjective optimization: fundamentals and an application in demand response
Speaker: Maria João Alves (Faculty of Economics, Univ. Coimbra)
In this talk, the fundamental concepts of multiobjective optimization and scalarizing techniques to compute nondominated solutions will be introduced. Scalarizing techniques consist of transforming the original multiobjective problem into a single objective problem that may be solved...

The moduli spaces of Higgs bundles
Speaker: André Oliveira (CMUP)
Given a Lie group G, the notion of G-Higgs bundle on a compact Riemann surface was introduced in the 1980s and 1990s by Nigel Hitchin. The algebraic varieties that parameterize these objects, i.e. their moduli spaces, have an extremely rich geometric and topological structure, yet are far...

Emergence of strange attractors from singularities
Speaker: Alexandre Rodrigues (CMUP, FCUP)
In this seminar, we explore some mechanisms to obtain strange attractors (with one or two positive Lyapunov exponents). We will discuss some open questions related to the existence of strange attractors near a special type of homoclinic cycle (associated to a bifocus). This seminar is...

A two-phase free boundary problem ruled by the infinity laplacian
Speaker: Damião Araújo (Universidade Federal da Paraíba, Brazil)
In this talk we discuss regularity aspects for solutions of a non-variational two-phase free boundary problem ruled by the infinity Laplacian. This is a joint work with E. Teixeira - University of Central Florida - USA and J.M Urbano - Universidade de Coimbra - PT....

Stone pseudovarieties
Speaker: Jorge Almeida (CMUP, Univ. Porto)
Profinite algebras have been extensively considered in the literature, particularly in the realms of groups and semigroups. They are the residually finite topological algebras over Stone spaces. In this talk, we consider classes of Stone topological algebras of a fixed signature that are...

Split extensions of monoids and Hopf algebras
Speaker: Florence Sterck (Université catholique de Louvain, Belgium)
In the category of groups, split extensions have a lot of interesting properties. One of them is the fact that the category of split extensions is equivalent to the category of group actions.Unfortunately, this property doesn't hold in the category of monoids. Nevertheless, it was proved in...

Thermodynamic formalism of non-uniformy expanding maps
Speaker: Paulo Varandas (UFBA & Univ. Porto)
Ergodic theory is the branch of dynamical systems which aims to describe the asymptotic behavior of almost all orbits, with respect to invariant measures.  However there are situations in which such a description is rather trivial, as the case when the invariant measures are finite...

A generalized approach to stochastic dominance
Speaker: Tommaso Lando (Univ. of Bergamo, Italy & VSB-TU Ostrava, Czech Republic)
In the theory of decision under uncertainty, ranking probability distributions with respect to the preferences of decision makers represents a major issue. In this context, the main ranking criteria are the first and the second-order stochastic dominance, FSD and SSD, respectively, due to...

Corruption cycles in democracy
Speaker: Alberto Adrego Pinto (FCUP)
In this talk, with the goal of analysing the evolution of corruption, we introduce an evolutionary game theoretic dynamical model describing the interaction of citizens with government and officials or bureaucrats of the state in a democratic country.We study and interpret the...

Dynamical systems from mutation-periodic quivers: definition and reduction by pre-symplectic tools
Speaker: Inês Cruz (CMUP, FCUP)
Cluster algebras and their associated quivers were introduced in 2002 by Fomin and Zelevinsky to provide a framework to study total positivity in matrix groups. Since then, cluster algebras have been successfully linked to a wide range of subjects including Poisson geometry, integrable...

Some challenging problems on numerical semigroups
Speaker: Manuel Delgado (CMUP, Univ. Porto)
A numerical semigroup is just a co-finite submonoid of the nonnegative integers, under addition. Despite being so simple mathematical objects, they hide very challenging combinatorial and computational problems (among others, coming from various areas of mathematics). The aim of the seminar...

Differential equations with two time-scales
Speaker: Isabel Labouriau (CMUP, Univ. Porto)
I'll discuss the role of different time-scales in differential equations and the associated geometry. This will be illustrated by a simple example, the FitzHugh-Nagumo equations, and by two of these equations coupled to form a system in ${\mathbb R}^4$. When two different time-scales are...

Novel applications of approximation theory to diverse problems in random matrices
Speaker: Nicholas Witte (Univ. Massey, New Zealand)
We take three contemporary problems arising from random matrices and show how approximation theory is crucial in solving them. However this is not merely an "off-the-shelf" application of known results from within approximation theory, but require extensions beyond the realm of its...

The prevalence of persistent tangles
Speaker: Pedro Lopes (IST, Univ. Lisboa)
This talk addresses persistent tangles. These are tangles whose presence in a knot diagram forces that diagram to be knotted. We provide newmethods for constructing persistent tangles. Our techniques rely mainly on the existence of non-trivial colorings for the tangles in question. Our main...

Frankl Conjecture
Speaker: André Carvalho (UC|UP PhD student)
This seminar will deal with a conjecture proposed in 1979 by Peter Frankl related to union-closed families of sets. Despite the fact that the conjecture regards finite union-closed families of sets, which appear to be very simple objects, very little is known about them. We try to present in...

Categorical semantics of intuitionistic linear logic
Speaker: Carlos Fitas (UC|UP PhD student)
The Curry-Howard-Lambek correspondence shows the deep connection between programs, proofs and morphisms in closed cartesian categories. It's natural to ask if similar results are true in other logics. Identifying the intuitionistic linear logic derivations up to the transformations in cut...

On entropy functionals associated with Bernstein stochastic processes
Speaker: Pierre Viullermot (Univ. Lorraine & Univ. Lisboa)
Bernstein processes constitute a generalization of Markov processes, and there are many equivalent ways to define them. In this talk I will show how to generate such processes from a hierarchy of forward-backward systems of decoupled deterministic linear parabolic partial differential...

An ageing ordering
Speaker: Beatriz Santos (UC|UP PhD student)
Many classes of lifetime distributions are characterized by their ageing properties, that can be described by their survival functions or by their failure rate functions. These ageing properties allow us to compare two distributions within the same family, giving rise to ageing orderings....

Ergodic theorems from topological and probabilistic viewpoints
Speaker: Lucas Amorim (UC|UP PhD student)
Ergodic theorems are classic measure theoretical results in dynamical systems or, more precisely, ergodic theory. They state that convergence of Birkhoff averages is typical, in a measure theoretical sense. This work aims to explain how these results can be reìnterpreted in light of...

The Picard group of the universal G-bundle over the moduli stack of pointed curves
Speaker: Filippo Viviani (CMUC/Roma Tre)
I will report on a joint work (in progress) with R. Fringuelli where we compute the Picard group of the moduli stack parametrizing pairs consisting of a smooth pointed curve C together with a G-principal bundleon C, for a given reductive algebraic group G....

Functorial semantics and descent II
Speaker: Fernando Lucatelli Nunes (CMUC, Univ. Coimbra)
Restricting our attention to the 2-category of categories, the main result of [1] gives in particular a natural factorization of functors via descent. Moreover, under suitable hypothesis, this factorization is shown to coincide with the semantic factorization of the functor. This gives as a...

Injectives via actions or: How I learned to stop worrying and love quantales
Speaker: Eros Martinelli (CIDMA, Univ. Aveiro)
In this talk, motivated by a classical result that relates injectives V-categories with injectives (= complete) ordered sets with an action, we prove a similar result for (L,V)-categories where L is the list monad....

Deep learning meets PDEs: an effective framework for image restoration
Speaker: Sílvia Barbeiro (CMUC, Univ. Coimbra)
Image restoration is one of the major concerns in image processing with many interesting applications. Partial differential equation (PDE) based models, namely of nonlinear diffusion type, are well-known and widely used for image noise removal. In this seminar we will describe a flexible...

Algebras associated to quivers
Speaker: Rui Prezado (UC|UP PhD student)
Given a small category I, its representation theory is, in essence, the study of the functor category [I,R-Mod] for some (not necessarily commutative) ring R. A case of interest is when we have I freely generated by a quiver Q. We construct an R-algebra RQ associated to this quiver Q in two...

Spectral analysis in the study of dynamical systems
Speaker: Raquel Couto (UC|UP PhD student)
After a brief journey into a class of Symbolic Dynamical Systems, that is related to Markov Chains, I will present the Limit Theorem for Markov Chains which can be obtained as a corollary of Perron Theorem (a spectral theorem in linear algebra). Next, we will see what may be taken as a...

Coupled cell networks and systems
Speaker: Ana Paula Dias (CMUP)
The aim of this talk is to introduce the connection between coupled cell networks and coupled cell systems. We also plan to address the issue of classifying networks from the dynamics point of view.  The seminar takes place in PORTO....

On nilpotent elements
Speaker: Miguel Gómez Lozano (Univ. Málaga, Spain)
See the attached file....

Padé and Padé-type rational and barycentric approximants
Speaker: M. Redivo-Zaglia (Univ. degli Studi di Padova, Italy)
We consider a particular case of the general rational Hermite interpolation problem where the value of a function f is interpolated at some points, and where the formal series expansions at the origin of the rational interpolant and of f agree as far as...

The homotopy type of shifted cotangent bundles
Speaker: Ricardo Campos (Univ. Montpellier, France)
Given a vector bundle E over a smooth manifold M, the algebra of functions on its shifted cotangent bundle T*[1]E has a natural structure of a Lie algebra and solutions of the Maurer-Cartan equation correspond to Lie algebroid structures on E. Allowing E to be a dg bundle (bundle of chain...

The Schützenberger involution on Kashiwara-Nakashima tableaux
Speaker: João Miguel Santos (CMUC, Univ. Coimbra)
The Schützenberger involution, due to Schützenberger, originally appeared in type A root system, using the model of semistandard Young tableaux. In this talk, we present a type C realization of the Schützenberger involution using the model of Kashiwara-Nakashima tableaux....

Algebraic and geometric classification of nilpotent Tortkara algebras
Speaker: Mykola Khrypchenko (Univ. Federal de Santa Catarina, Brazil)
We classify all nilpotent Tortkara algebras of dimension 6 over the field of complex numbers. We also determine the rigid algebras and irreducible components of the variety of such algebras. This is a joint work with Ilya Gorshkov (Sobolev Institute of Mathematics) and Ivan Kaygorodov...

Parametric Presburger arithmetic
Speaker: Tristram Bogart (Univ. de los Andes, Colombia)
Parametric Presburger arithmetic concerns families of sets defined using quantifiers and Boolean combinations of formulas of the form a(t)·x ≤ b(t), where a(t) ∈ Z[t] d , b(t) ∈ Z[t]. In the quantifier-free these formulas represent sets of integer points in families of...

The geometry of generalized flat ribbons
Speaker: Matteo Raffaelli (CMUC)
In this talk we will be studying the problem of approximating -- locally along a curve -- a given surface S in three-space by a developable (i.e., flat) one. Naturally, we will consider tangent approximations, where the approximating strip-shaped surface, or ribbon, has the same distribution...

Normally ordered forms of powers of differential operators
Speaker: Samuel Lopes (CMUP, Univ. Porto)
See the attached file....

Sequence Morrey space and Pitt's type theorem

Leszek Skrzypczak (Adam Mickiewicz Univ., Poznan, Poland)

Morrey (function) spaces and, in particular, smoothness spaces of Besov-Morrey or Triebel-Lizorkin-Morrey type enjoyed a lot of interest recently. Here we turn our attention to Morrey sequence spaces mu,p =mu,p(Zd), 0<p\leq u<\infty, which have yet been considered almost nowhere. They...

On the dimension formula for Goldie's uniform dimension
Speaker: Christian Lomp (Univ. Porto)
A classical (right) ring of fractions of a ring R is an overring Q(R) of R such that any non-zero divisor of R is invertible in Q(R) and any element of Q(R) is of the form ab^{-1} for a and b elements of R with b a non-zero divisor. Oystein Ore proved in the 30s that a (non-commutative)...

Introduction to causal analysis
Speaker: Maria Králová (Masaryk Univ., Czech Republic)
Researchers in many areas where only observational data are available often face the challenge of assessing the effect of the treatment on the outcome.  Within a framework of traditional statistical analysis of multivariate data, only different measures of association are available....

Regularity for elliptic equations under minimal assumptions
Speaker: Giuseppe Di Fazio (Università di Catania, Italy)
Elliptic PDEs are ubiquitous in Mathematics and Sciences. A very important topic concerning elliptic PDEs is the regularity of solutions. We will review some regularity results for linear and quasilinear uniformly elliptic equations. The main focus will be on the minimal assumptions we need...

Recent thoughts about the NIEP
Speaker: Charles Johnson (College of William and Mary, Williamsburg, USA)
We discuss 3 topics about the nonnegative inverse eigenvalue problem about which recent progress has been made. These include 1) ruling out certain spectra for the 5-by-5 S-NIEP; 2) Jordan structure for realizable spectra with repeated eigenvalues; and 3) the doubly stochastic single...

Feedback invariants of series connected systems and LR coefficients
Speaker: Marija Dodig (Univ. Lisboa)
In this talk we shall describe the possible feedback invariants of linear systems obtained as a result of series connections of two linear systems. This corresponds to a completion problem for matrices. We solve the problem in a generic case, and we conjecture general solution. It turns...

Spin-orbit coupling in the Solar System
Speaker: Alexandre C. M. Correia (DFUC, Univ. Coimbra)
Recent developments in the study of the Solar System dynamics have shown that it is not such a quiet place. Mutual interactions between all bodies may destabilise the orbits and the spins of all terrestrial planets and satellites. Chaotic motion is everywhere and our present quiet Earth will...

Lagrangian systems with external forces preserving geometric structure
Speaker: David Martin de Diego (ICMAT, Madrid, Spain)
In this talk we will discuss the geometric description of mechanical systems with external forces. Some of these systems has additional geometric features and we will study if it is possible to preserve some of these properties using geometric integrators like variational integrators...

Colimit-dense subcategories
Speaker: Jiří Adámek (Tech. Univ. Braunschweig, Germany)
A small full subcategory K' of a category K is called dense (or colimit-dense) if every object X of K is a colimit of some diagram in K' (or is the canonical colimit of all maps from objects of K' to X, resp.). The existence of a colimit-dense subcategory is an important property, e.g., the...

Crossed semimodules of cancellative conjugation monoids
Speaker: Nelson Martins Ferreira (CDRSP, ESTG, IP Leiria)
This talk is based on the work [1] where we show that the category of cancellative conjugation semigroups is weakly Mal'tsev and give a characterization of all admissible diagrams there.In the category of cancellative conjugation monoids we describe, for Schreier split epimorphisms with...

Dynamics, symmetry and patterns: a tour of Einstein, Ginzburg and Landau
Speaker: Phillipo Lappicy (USP, Brazil, and IST, Lisbon)
This talk will present my recent results in certain directions within the realm of partial differential equations. On one hand, parabolic equations generate a semiflow in infinite dimensions, and hence we are interested in the dynamical question: what happens when time is large? We will...

Rees algebras of modules
Speaker: Ana Luísa Correia (Academia Militar and CEAFEL - FCUL)
The Rees algebra of an ideal may be seen as a coordinate ring of a projective variety and it plays an important role in the study of algebraic singularities. Many parts of this theory can also be extended to the case of filtrations ideals or modules, as well to the case of the multi-Rees...

Describing the singular behaviour of parabolic equations on cones in fractional Sobolev spaces
Speaker: Cornelia Schneider (Univ. Erlangen-Nuremberg, Germany)
This talk focusses on the smoothness of the solutions of parabolic PDEs on Lipschitz domains in the fractional Sobolev scale Hs, s in R. The regularity in these spaces is related with the approximation order that can be achieved by numerical schemes based on uniform grid refinements. The...

Geometric constructions: some working hypotheses
Speaker: Graziani Pierluigi (Univ. of Urbino Carlo Bo, Italy)
Among the many theses regarding the nature of Greek mathematics, the most popular one held by historians and philosophers of ancient mathematics is that Greek mathematics, in particular Euclid's Elements, has a constructive nature. However, it is not always clear what the defenders of this...

Peregrine's system revisited
Speaker: Ángel Durán (Univ. Valladolid, Spain)
In 1967, D. H. Peregrine proposed a Boussinesq-type model for long waves in shallow waters of varying depth (Peregrine, J Fluid Mech 27:815-827, 1967). This prominent paper turned a new leaf in coastal hydrodynamics along with contributions by Serre (La Houille Blanche 8:374-388, 1953) and...

Decidability of first-order theories
Speaker: Cristina Sernadas (CMAFcIO, Univ. Lisboa)
Some results and reduction techniques for proving decidability of mathematical theories and completeness of logics are presented. The crucial role of the theory of real closed ordered fields is explained. Selected illustrations from Euclidean Geometry to Quantum Logic are discussed....

Evolutionary quasi-variational and variational inequalities with constraints on the derivatives
Speaker: Lisa Santos (Univ. Minho)
We study  the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination of partial derivatives of the solutions. The quasi-linear operators are of monotone type,...

On some applications of orthogonal polynomials in Mathematical-Physics
Speaker: Renato Álvarez-Nodarse (Univ. Sevilla, Spain)
The orthogonal polynomials (OP) are very useful tools in solving problems not only in Mathematics but also in Physics and Engineering. Among them, the classical orthogonal polynomials (COP) deserve a special attention. The main reasons are, from my point of view, from one hand the fact that...

The finite element method in sheet metal forming simulation
Speaker: Diogo Neto (DEM, Univ. Coimbra)
Numerical simulation is an indispensable tool for the successful implementation of digital manufacturing. The actual requirements for a higher degree of product customization dictate the use of simulation, allowing the virtual testing and validation of product, process and system design....

On finite simple quotients of triangle groups
Speaker: Claude Marion (CMUP, Univ. Porto)
See the attached file...

Stochastic solutions for nonlinear partial differential equations
Speaker: Rui Vilela Mendes (CMAFCIO, Univ. Lisboa)
A stochastic solution of a pde is a stochastic process that started from a point in the domain, generates a boundary measure which, when integrated over the initial condition, provides a local solution of the equation. Stochastic solutions not only provide new exact solutions for nonlinear...

On the classification of Schreier extensions of monoids with non-abelian kernel
Speaker: Andrea Montoli (Univ. degli Studi di Milano, Italy)
We will show that any regular right Schreier extension of a monoid M by a monid A induces an abstract kernel, i.e. a monoid homomorphism from M to the factor monoid End(A)/Inn(A). If an abstract kernel factors through Epi(A)/Inn(A), then we associate to it an obstruction, which is an element...

Order-enriched solid functors
Speaker: Lurdes Sousa (CMUC and IP Viseu)
Order-enriched solid functors enjoy many of the properties of their counterparts, including the detection of weighted colimits. We study two slightly different notions of order-enriched solidity and present several examples, which include functors of general varieties of ordered algebras and...

Portfolio selection in evolutionary algorithms
Speaker: Andreia P. Guerreiro (CISUC, DEI-UC)
Evolutionary Algorithms (EAs) are algorithms inspired on the process of natural selection, and are among the most popular methods in multiobjective optimization. One of the main steps of an EA is selection which is aimed at focusing on the best individuals, but must also maintain a...

On function theory in the Euclidean space
Speaker: Klaus Gürlebeck (Bauhaus-Universität Weimar, Germany)
We consider a function theory for functions defined in Rn with values in the quaternions or in Clifford algebras. The class of monogenic functions is firstly defined as the set of null solutions of a generalized Cauchy-Riemann system. Basic elements of this function theory (see also...

Geometry of mechanical control systems with applications
Speaker: Sandra Isabel Ventura Ricardo (UTAD, Vila Real)
In this talk, a geometric setting for studying mechanical control systems is presented. A special class is distinguished: the class of geodesically accessible mechanical systems, for which the uniqueness of the mechanical structure is guaranteed (up to an extended point transformation)....

The 2-representation theory of Soergel bimodules of finite Coxeter type: a road map to the complete classification of all simple transitive 2-representations.
Speaker: Marco Mackaaij (Univ. Algarve)
I will recall Lusztig's J-categories, which are fusion categories obtained from the perverse homology of Soergel bimodules. For example, for finite dihedral Coxeter type this fusion category is the semisimplified quotient of the module category of quantum so(3) at a root of unity, which...

From quantum to quantales and beyond
Speaker: Pedro Resende (CAMGSD, Univ. Lisboa)
[The following abstract may also be found in the PDF file that is attached to this announcement] The axioms of quantum mechanics laid out by von Neumann involved Hilbert spaces and operators on them, and it soon became apparent that the properties of collections of operators are...

Axiom \(T_D\) and the Simmons sublocale theorem
Speaker: Jorge Picado (CMUC, Univ. Coimbra)
A topological space \( X \), more precisely its associated frame \( \Omega(X) \) of open sets, has typically more sublocales than subspaces.  We will analyze some of Simmons (1980) and Niefield and Rosenthal (1987) results concerning sublocales induced by subspaces. The first result...

Tree oriented pullbacks
Speaker: Flávio Ulhoa Coelho (Univ. São Paulo, Brazil)
See the attached file....

Functorial semantics and descent
Speaker: Fernando Lucatelli Nunes (CMUC, Univ. Coimbra)
In [1], given a 2-category A satisfying suitable hypothesis, we give the semantic factorization via descent. This specializes to a new connection between monadicity and descent theory, which can be seen as a counterpart account to the celebrated Bénabou-Roubaud Theorem [2]. It also...

Compactly generated (T,V)-spaces
Speaker: Willian Ribeiro (PhD Student, CMUC)
First studied by Hurewicz, compactly generated spaces arise as a convenient category for homotopy theory and algebraic topology [1]. The full subcategory of Top (the category of topological spaces and continuous functions) formed by the latter spaces is well-known to have nice properties: it...

Variational theory and spectral geometry of quantum graphs
Speaker: James Kennedy (Univ. Lisboa)
The past decade has seen a pronounced growth of interest in differential operators defined on metric graphs, commonly known as quantum graphs. They offer the technical simplicity of one-dimensional objects, while often displaying complex behaviour akin to higher-dimensional ones, and are...

Truncated boolean representable simplicial complexes
Speaker: Pedro V. Silva (CMUP, Univ. Porto)
These structures constitute the largest known class of simplicial complexes admitting a geometric/topological theory. We will present the main features of this class and some recent results (joint work with Stuart Margolis (Bar-Ilan) and John Rhodes (Berkeley))....

Information lost when resampling
Speaker: Tilo Wiklund (Univ. of Uppsala, Sweden)
Various procedures in statistics rely on taking decisions based on data that has been resampled (usually with replacement). Examples include bootstrap-based confidence bounds and error estimates or "bagged" estimators. Since resampling is an additional source of randomness such...

Superalgebras with superinvolution
Speaker: Herlisvaldo Costa Santos (UC|UP PhD programme student)
Our objective in this work is to provide primitive associative superalgebras a structure analogous to those for the algebras and to classify primitive superalgebras with superinvolution having a minimal superideal....

Homological invariants of blocks of Schur algebras
Speaker: Steffen Koenig (Univ. Stuttgart, Germany)
Let S(n,r) be a classical or quantised Schur algebra with n ≥ r. Totaro determined the global dimension of classical S(n,r) and Donkin extended this result to quantum S(n,r). Ming Fang and I have determined the dominant dimension (which in some sense measures the strength of Schur-Weyl...

Representation type of algebras and quivers
Speaker: Ivan Yudin (CMUC, Univ. Coimbra)
One of the first results one encounters in the standard university courses of algebra are classifications of equivalence classes of matrices under various transformations. If we are allowed to multiply the matrix in question from each side with an invertible matrix, then the corresponding...

On the topological complexity of surfaces
Speaker: Lucile Vandembroucq (Univ. do Minho)
In this talk, we will consider the concept of topological complexity introduced by M. Farber to give a measure of the motion planning problem and discuss it for surfaces. In particular, we will see that the topological complexity of the Klein bottle and higher genus non-orientable surfaces...

Generalized weighted Lorentz spaces
Speaker: Amiran Gogatishvili (Czech Academy of Sciences, Prague, Czech Republic)
We will define a new class of generalized weighted Lorentz spaces and we will present some properties of these spaces....

A mathematical model for a plant circadian oscillator
Speaker: Adérito Araújo (CMUC, Univ, Coimbra)
Circadian rhythms are generated at the cellular level by a small but tightly regulated genetic network. They are observed in most organisms on earth and are known to play a major role in successful adaptation to the 24-h cycling environment. Understanding the molecular basis of cellular...

On the linear nature of pseudowords
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
In this talk we see how the pseudowords in a finitely generated free profinite aperiodic semigroup are faithfully represented by labeled linear orders induced by factorizations of the pseudowords.This is joint work with Jorge Almeida, José Carlos Costa and Marc Zeitoun. ...

Kippenhahn's Theorem
Speaker: Stephan Weis (CMUC, Univ. Coimbra)
The numerical range of a matrix is a convex subset of the plane of complex numbers (Toeplitz 1919, Hausdorff 1919) and equals the convex hull of a real algebraic curve (Kippenhahn 1951, Chien and Nakazato 2010). An interesting higher-dimensional analogue would be to write the joint...

Riemann-Hilbert problems in the theory of orthogonal polynomials
Speaker: Amílcar Branquinho (CMUC, Univ. Coimbra)
In this talk we survey different aspects of the theory of orthogonal polynomials.Due to the ubiquity nature of orthogonal polynomials in modern science, their study has been performed from very many different points of view. Indeed, they can be considered from a purely algebraic point of...

On the existence of solutions for inextensible string equations
Speaker: Ayk Telciyan (UC|UP PhD programme student)
In this talk, we analyze existence of solutions for inextensible string equations. In particular, we have results in two directions.On one hand, we find explicit traveling wave solutions for a system of hyperbolic conservation laws resulting from inextensible string equations via suitable...

Representations of fundamental groups of surfaces
Speaker: Peter Gothen (CMUP, Univ Porto)
We consider representations of the fundamental group of a closed surface in the group SL(2,R). To each such representation one can associate an integer invariant called the Toledo invariant. A theorem of J. Milnor says that the absolute value of the Toledo invariant is less than or equal to...

Campanato spaces and applications in partial differential equations
Speaker: David Jesus (UC|UP PhD Programme student)
In this talk I will discuss a generalization of Campanato's characterization of Holder continuity, and use these results to study the regularity of solutions to the non-homogeneous p-Laplace equation....

Boolean representable simplicial complexes
Speaker: Maria Inês Couto (UC|UP PhD Programme student)
In this seminar we will discuss some properties of a particular class of simplicial complexes from a purely combinatorial perspective. The elements of this class, including all the matroids, admit a representation by a matrix with entries in the boolean semiring, so they are said boolean...

Lattice decomposition of modules and decomposition of categories
Speaker: Pascual Jara (Univ. de Granada, Spain)
The decomposition of a module M in a direct sum M=M1+M2 does not produce, in general, a decomposition of the lattice L(M) of all submodules in a direct product of lattices L(M)=L(M1)xL(M2). When this happens we say M=M1+M2 is a lattice decomposition. These particular decompositions have...

Actions of Hopf algebras
Speaker: Christian Lomp (CMUP, Univ Porto)
Group algebras and enveloping algebras of Lie algebras are examples of Hopf algebras. Automorphisms acting on rings as well as derivations acting on them are examples of Hopf algebra actions. Guided by these classical examples, we will motivate the study of Hopf algebra actions and consider...

Porous medium equations with advection
Speaker: Nicolau Diehl (CMUC)
In this talk we present two types of results: one about decay estimates and another about global existence. Both results are obtained for bounded weak solutions of the Cauchy problem for Porous Medium Equations with advection through a fundamental energy estimate, an L^p -L^q estimate, and...

Categories, allegories
Speaker: Igor Arrieta (UC|UP PhD programme student)
A binary relation from a set A to a set B is a subset of the cartesian product AxB. Moreover, a function f: A->B can be identified with a particular type of relation, namely the relation consisting of pairs (x,f(x)). Consequently, the usual category of sets can be regarded as a...

Geodesics in the space of Kähler metrics
Speaker: Pedro Silva (UC|UP PhD programme student)
A Kähler manifold is a differentiable manifold with three geometric structures: a Riemannian metric, a symplectic form, and a complex structure, satisfying some compatibility conditions. The metrics and the symplectic forms for which these compatibility conditions are satisfied are...

Identification and simulation of flow in heterogeneous media: a model for oil extraction
Speaker: Hugo Peña Gomez (UC|UP PhD Programme student)
The models of double porosity-permeability are used to described the dynamics of oil extraction (porous medium). The talk will be about presenting some aspects of this kind of models and a variation considering a particular medium structure. Some numerical results will be exposed. ...

On the group of a rational maximal bifix code
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
A code is a set of words that freely generates a free submonoid of the free monoid. A specially relevant place in the theory of codes is occupied by the maximal bifix codes.In the last years, attention has been given to a process of "localization" in which one looks at the...

What is ... Pointfree Topology?
Speaker: Jorge Picado (CMUC, Univ. Coimbra)
Pointfree topology deals with frames and locales, the pointfree counterparts of topological spaces. We shall present motivation for this approach to topology and its basic features and facts. We will emphasize some of the main differences between the two approaches and some advantages of the...

Leibniz algebras with invariant forms
Speaker: Said Benayadi (Univ. de Lorraine, Metz, France)
In the case of Lie algebras, the left (resp. right) invariance of bilinear forms is equivalent to the invariance (or associativity) of these forms. However, it is not the case for Leibniz algebras.In this talk, we will give some results on the structures of Leibniz algebras which are...

The existence theorem of weak solution for the initial-boundary problem for Oskolkov's system of equations
Speaker: Mikhail Turbin (Voronezh State Univ., Russia)
In the talk, the existence of weak solutions of the initial-boundary value problem describing the motion of weakly concentrated aqueous solutions of polymers (Oskolkov's system) is proved. The proof is based on the approximation-topological approach. On the first step, the operator equation...

Asymptotic theory of set partitions: a representation theory agenda
Speaker: Jocelyn Lochon (Univ. Lisboa)
See the attached file....

3-manifolds, knots and surfaces
Speaker: João Miguel Nogueira (CMUC, Univ. Coimbra)
We will survey the motivation and history of 3-manifold topology, together with its twin subject of knot theory, giving special emphasis to the importance of surfaces on the understanding of these subjects. Under this framework, we will also review contributions of the speaker as suitable....

The numbers lead a dance
Speaker: Poul Hjorth (Technical Univ. of Denmark, Lyngby, Denmark)
The unfolding of some strictly syntax based poetry is viewed from the perspective of dynamical systems theory. I will provide examples of this, in particular of a type of 13th century lyrical style, the generalisation of which gives rise to mathematical questions. In the search for answers...

Performance estimation of first-order methods for composite convex optimization
Speaker: François Glineur (Université catholique de Louvain, Belgium)
Composite convex optimization consists in the minimization of a convex objective function equal to the sum of several convex functions with different properties, for example a smooth term and a nonsmooth term. We consider a large class of first-order methods designed to solve such...

Applied Mathematics: applications in biomedicine and biomathematics
Speaker: Isabel Narra de Figueiredo (CMUC, Univ. Coimbra)
This talk focus on the description of some computer-assisted methods we have developed for the automatic interpretation of medical images and on some biomathematics models we have proposed to represent and simulate the early stages of colon cancer....

Limit groups and their profinite completion
Speaker: Theo A. D. Zapata (Univ. de Brasília, Brazil)
In the last decades limit groups have been attracting the attention of many mathematicians, specially because they played a fundamental role in the recent solution of the outstanding Tarski problem on free groups. Two simple group-theoretical reasons for so much attention are the following:...

A categorical model for the Hopf fibration
Speaker: Björn Gohla (GFM, Univ. Lisboa)
We give a description up to homeomorphism of S3 and S2 as classifying spaces  of small categories, such that the Hopf map S3 --> S2 is the realization of a  functor....

Investigation of the dynamics of the anti-Zener model
Speaker: Vladimir Orlov (Voronezh State Univ., Russia)
We prove the solvability in the weak sense of the initial-boundary value problem for the multidimensional fractional model generated by the one-dimensional anti-Zener model. This model takes into account the prehistory of fluid motion along the particle trajectories. This model well...

Computing the indecomposable representations of left regular bands
Speaker: Herman Goulet-Ouellet (UC|UP PhD programme student)
Left regular bands are a family of semigroups that enjoy many surprising properties. They have received some attention recently due to their link with Markov chains and hyperplane arrangements. In this talk, we will see how to compute the indecomposable projective representations of finite...

The boolean reflection of a frame and the Cantor-Bendixson derivative
Speaker: Ana Belén Avilez (UC|UP PhD programme student)
We consider two categories, the category of frames and the category of complete boolean algebras. We know that a complete boolean algebra is always a frame, but we want to assign universally a complete boolean algebra to each frame. It turns out this is not always true, but there is a result...

Nonassociative products in nonassociative algebras with involution
Speaker: Jose Ramón Brox López (CMUC)
Starting from the variety of associative, Lie, Jordan, or alternative algebras with involution (or involutive automorphism), we classify all the formal bilinear products of the formaxy+bx*y+cxy*+dx*y*+Ayx+Byx*+Cy*x+Dy*x*,formed with the help of the original product and the involution *...

Jacobi multipliers and nonholonomic Lagrangian systems
Speaker: Patrícia Santos (ISEC, Coimbra)
Jacobi multipliers is a tool in the solution of problems in mechanics that provides Lagrangians descriptions and constants of motion for systems of ODE. In this seminar we establish the relation between Jacobi multipliers and nonholonomic Lagrangian systems where the dynamics is determined...

Polynomial mappings and sieved ultraspherical polynomials. An application involving an electrostatic model
Speaker: Márcio N. de Jesus (IP Viseu)
We consider orthogonal polynomials (OP) via polynomial mappings in the framework of the semiclassical class. In particular, we analyze in detail cubic transformations for semiclassical OP of class at most 2, giving new examples of semiclassical OP of class 2 and providing integral...

Besov regularity of parabolic PDEs
Speaker: Cornelia Schneider (Univ. Erlangen-Nuremberg, Germany)
The talk is concerned with the regularity of  solutions to linear and nonlinear evolution equations on nonsmooth domains.   In particular, we study the smoothness in a specific scale of Besov spaces. The regularity in these spaces determines the approximation order that...

Efficient and accurate Lagrangian-Eulerian numerical schemes for solving hyperbolic balance laws
Speaker: Eduardo Abreu (UNICAMP, Brazil)
We develop first-order and high-resolution stable-fast numerical schemes for hyperbolic balance law models. A key feature is the dynamic tracing forward of the integral curves, which are locally conservative and preserve the natural setting of weak (entropic) solutions linked to the...

Numerical modelling of cell-renewal, pit patterns and crypt fission in colonic crypts
Speaker: Giuseppe Romanazzi (UNICAMP, Brazil)
The colonic epithelium is filled in its internal walls by small cavities called crypts. These crypts are small tubular glands, containing proliferative cells, that obey to a programmed cell mechanism. The aberrant crypts occur as a consequence of an abnormal behavior of this programmed...

An Eilenberg-like Theorem beyond regular languages
Speaker: Célia Borlido (Univ. Nice Sophia-Antipolis, France)
(See the attachment for the pdf version of the abstract).  Finite and profinite monoids have proved to be a powerful tool in the study of regular languages. On the one hand, Eilenberg's correspondence, establishing a bijection between certain classes of regular languages (so-called...

On the Clebsch-Gordan problem in positive characteristic
Speaker: Stephen Donkin (Univ. of York, UK)
This is joint work with Samuel Martin. Consider the special linear group G of degree 2, over the complex numbers. There is one rational irreducible G-module V(r) for each non-negative integer r. The module V(r) has dimension r+1 and may be realised as the rth symmetric power of the...

Galois theory of graphs
Speaker: George Janelidze (Univ. Cape Town, South Africa)
This talk is about graphs in the sense of graph theory (not in the sense used in category theory). It will be shown that their Galois theory is not very different from other set-valued combinatorial Galois theories considered before, in spite of what it seems, due to non-existence of various...

On generating cartesian closed subcategories of (T,V)-Cat
Speaker: Willian Ribeiro (PhD Student, CMUC)
Generalizing the work of [1], we present the process of generating cartesian closed subcategories of (T,V)-Cat. From a fixed class C of objects, we form a new (reflective) subcategory whose objects are shown to be colimits of objects in C. For instance taking for C the class of compact...

Towards semi left exactness and Janelidze-Galois within the lax idempotent context
Speaker: Fernando Lucatelli Nunes (CMUC)
This is a joint work with Maria Manuel Clementino. Our aim is to understand the analogues of semi-left exactness and the analogues of the basic ideas of Janelidze-Galois within the lax idempotent context. As it is usual, there are more than one possible approach to do so. Our first...

Tree conjecture on graphs and more colourings in polytopes
Speaker: Raul Penaguião (Univ. Zurich, Switzerland)
We will talk about some chromatic invariants in graphs and polytopes, and see what are the consequences of a nice description of the kernel of these chromatic maps in important problems like the tree conjecture. We will see that the most general version of this problem is in the realm of...

Infinitesimal automorphisms of VB groupoids and algebroids
Speaker: Alfonso Tortorella (KU Leuven, Belgium)
VB-groupoids and algebroids are vector bundle objects in the categories of Lie groupoids and Lie algebroids respectively, and they are related via the Lie functor. VB-groupoids and algebroids play a prominent role in Poisson and related geometries. In this talk, based on joint work with...

A problem-dependent inner approximation of the completely positive cone

Mina Saee Bostanabad (PhD student, CMUC)

Motivated by the expressive power of completely positive programming and its dual, copositive programming, to encode hard optimization problems, many approximation schemes for the completely positive and copositive cones have been proposed and successfully used. For the completely positive...

Aspects of the Painlevé equations
Speaker: Galina Filipuk (Univ. of Warsaw, Poland)
In this talk I shall present new nonlinear differential-difference equations related to the second Painlevé equation. I shall also review the basics of Nevanlinna theory (notation, examples and main theorems) and show how it can be applied to the study value distribution and growth...

Totally nonnegative unitriangular Toeplitz matrices and k-Schur functions
Speaker: Cédric Lecouvey (Univ. François Rabelais, Tours, France)
The talk will focus on effective parametrisations of unitriangular Toeplitz matrices. We will first recall Thoma's parametrisation for the infinite matrices. Next, for matrices of rank k, we will see how one can recover Rietsch's parametrisation by k-tuple of nonnegative reals from the...

Spectral properties of variable-coefficient Toeplitz matrices
Speaker: Helena Mascarenhas (CEAFEL, IST Lisboa)
Finite sections of classical Toeplitz matrices have been heavily studied in the last decades due to its several applications in particular to engineering problems. Variable-coefficient Toeplitz matrices generalize these ones. We will present results on the asymtotic behaviour of the ...

A new look at Calculus: how an old idea naturally leads from simple Algebra to the heart of Analysis
Speaker: R. Michael Range (State University of New York at Albany, USA)

Supercharacters for algebra groups and their geometric relations
Speaker: João Dias (Univ. Lisboa)
Given any algebra group over any finite field one has a supercharacter theory constructed by P. Diaconis and I.M. Isaacs. And we may ask three questions:- How the supercharacter theory behaves with respect to change of field (i.e. finite field extensions)- Exists an object that contains all...

Mining chemical space for pharmacological rules: corneal permeation as an example

Rui M. M. Brito (BSIM Therapeutics, IPN & Univ. Coimbra) and João H. B. Meireles (BSIM Therapeutics, IPN)

Drug discovery and development is a complex, long and expensive process involving searches in a multidimensional space and multi-objective optimization based on apparently unrelated target functions. The discovery of a new "small molecule" medicine depends on the identification of...

Supercharacters, Schur rings and association schemes
Speaker: Carlos André (Univ. Lisboa)
In this talk, we describe and illustrate the connection of supercharacter theories of finite groups with Schur rings and association schemes, and we discuss possible generalisations to the context of (infinite) topological groups, in particular of totally disconnected compact and locally...

On the profinite topology on solvable groups
Speaker: Khadijeh Alibabaei (CMUP, Univ. Porto)
We show that the wreath product of a finitely generated abelian group with a polycyclic group is a LERF group. This theorem yields as a corollary that the finitely generated free metabelian group is LERF, a result due to Coulbois.We also show that the finitely generated free solvable group...

Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle
Speaker: Kenier Castillo (CMUC)
The purpose of this talk is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix similar to a unitary upper Hessenberg matrix ...

Supercharacters of unitriangular groups and ramification graphs
Speaker: Filipe Gomes (Univ. Lisboa)
Supercharacter theories are generalizations of the usual character theory of a group. In this talk, we present the basics of supercharacter theory, emphasizing the supercharacter theory of the unitriangular groups and its combinatorial interpretations. In the second part of the talk, we...

Identities in plactic and related monoids
Speaker: António Malheiro (Univ. Nova de Lisboa)
The plactic monoid is a fundamental algebraic object which captures a natural monoid structure carried by the set of combinatorial objects of semistandard Young tableaux. Other monoids arise in a similar way by considering different combinatorial objects: the hypoplactic monoid...

The nine lemma in the S-Mal'tsev and in the S-protomodular settings
Speaker: Andrea Montoli (Univ. degli Studi di Milano, Italy)
We investigate what is remaining of the nine lemma and of the denormalized nine lemma, respectively valid in a pointed protomodular and in a Mal'tsev category, in the context of partial protomodular and partial Mal'tsev categories, relatively to a class S of points. The results apply, among...

On homology monoids of simplicial abelian monoids
Speaker: Alex Patchkoria (A. Razmadze Math. Institute of Tbilisi State Univ., Georgia)
The homology semimodules Hn(S) of a presimplicial semimodule S introduced in our earlier paper, are studied in the case where S is a simplicial abelian monoid. In particular, it is shown that if a simplicial abelian monoid A satisfies the Kan condition and the monoid of path components...

Mathematics and the world around us
Speaker: Renato Álvarez-Nodarse (IMUS, Univ. Sevilla, Spain)
In 1623 Galileo wrote a beautiful book entitled “Il Saggiatore" in which appeared his famous statement that mathematics is the language of science. He claimed that to understand the Universe it is necessary to understand the language in which it is written, and it is written in...

Minimum energy curves in fluid environments
Speaker: Luis Machado (ISR/UC and Univ. Trás-os-Montes e Alto Douro)
In path planning problems of autonomous underwater or aerial vehicles is frequently required to find a mission path that minimizes acceleration and drag while a vehicle moves from an initial position to a final target.Drag is a mechanical force that characterizes the resistance that the...

Entropy numbers of compact embeddings or radial and multi-radial subspaces of Sobolev spaces with applications.
Speaker: Leszek Skrzypczak (Adam Mickiewicz Univ., Poznan, Poland)
See the attached file...

Price models in mean-field games

Diogo Gomes (KAUST, Saudi Arabia)

In this talk, we introduce a price-formation model for electricity markets where a large number of small players can store and trade electricity. Our model is a constrained mean-field game (MFG) where the price is a  Lagrange multiplier for the supply vs. demand balance condition. Under...

Rewriting systems and commutativity of diagrams
Speaker: Ivan Yudin (CMUC, Univ. Coimbra)
It is a common situation that given a set of commutative diagrams one needs to establish commutativity of another set of diagrams. The naive approach to the problem is to partition each diagram into smaller diagrams, so that each subdiagram is in the given set of commutative diagrams.In the...

Topological groups have representable internal actions
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
The actions of a group B on a group X correspond bijectively to the group homomorphisms from B to the group of automorphisms of X. This can be stated using representability of the functor 'actions on X' (see [2, 3]).In this talk we show the corresponding result for topological groups: The...

Sets of operators determined by the numerical range

Janko Bracic (Univ. of Ljubljana, Slovenia)

See the attached file....

Some results on minors of Toeplitz matrices and the theory of symmetric functions
Speaker: Miguel Tierz (Univ. Lisboa)
We study minors of Toeplitz matrices using the theory of symmetric functions. The symbols of the Toeplitz matrices can either be in the Szegö class or have Fisher-Hartwig singularities and the results apply both to minors of finite and of large dimension. As an application, and also...

Multiscale non-helical dynamos
Speaker: Roman Chertovskikh (SYSTEC, Univ. Porto)
In this talk a short introduction to the magnetic dynamo theory (explaining how magnetic fields can be produced by flows of an electrically conducting fluid) as well as recent advances made by the speaker and his collaborators will be presented. Generation of large-scale magnetic field by...

A tour in extreme value laws
Speaker: Jorge Soares (UC|UP PhD student)
In this talk, we analyse the stochastic process that arises from a dynamical system by evaluating an observable function along a given orbit of the system. Our goal is to give sufficient conditions for the existence of an Extreme Value Law for the considered process. We will present an...

Product formulas, generalized convolutions and integral transforms
Speaker: Rúben Sousa (UC|UP PhD student)
It is well-known that the ordinary convolution is closely related with the Fourier transform. It is therefore natural to ask: for other important integral transforms, can we define generalized convolution operators having analogous properties? Actually, the answer depends on the existence of...

Phaseless rank and amoebas
Speaker: António Goucha (UC|UP PhD student)
The phaseless rank of a nonnegative matrix M is defined to be the least k for which there exists a complex matrix N such that |N| = M, entrywise speaking. In optimization terms, it is the solution to the rank minimization of a matrix under phase uncertainty on the entries. This concept has a...

On the regularity of the vanishing ideals of graphs
Speaker: Jorge Neves (CMUC, Univ. Coimbra)
In 2011, Renteria, Simis and Villarreal introduced a new class of binomial ideals associated to graphs. One associates to a simple graph, G, the vanishing ideal of a subset of a projective space over a finite field, parameterized by the edges of the graph. Although originally these ideals...

Numerical simulation of wave propagation from deep waters to very shallow waters, including changes over real bottoms
Speaker: José Simão Antunes do Carmo (Department of Civil Engineering, University of Coimbra)
See the attached file...

A class of electromagnetic p(x,t)-curl systems: existence and uniqueness, blow-up and finite time extinction
Speaker: Stanislav Antontsev (Univ. Lisboa & Inst. Hydrodynamics, Novosibirsk, Russia)
See the attached file...

On basic Fourier-Bessel expansions. Some related issues.
Speaker: José Luis Cardoso (CM-UTAD)
We will present a summary of the latest developments with respect to expansions involving the Third Jackson q-Bessel function (or, Hahn-Exton q-Bessel function), with special emphasis regarding Fourier expansions related to some basic functions which are q-analogues...

Global higher regularity of solutions to p(x,t)-parabolic equations
Speaker: Ivan Kuznetsov (Institute of Hydrodynamics, Novosibirsk, Russia)
See the attached file...

Application of data mining to structural biology
Speaker: Irina S. Moreira (Center for Neuroscience and Cell Biology, Univ. Coimbra)
Contrary to the reductionist approach aimed at understanding individual components, the new data revolution allows the understanding of complicated interactions and pathways through the use of statistical Data Mining (DM). This is an active area of research in mathematic/computer science...

The intricacies of algebraic power series
Speaker: Herwig Hauser (Univ. of Vienna, Austria)
A formal power series h(x) = sum a_n x^n is called algebraic if it satisfies a polynomial equation with coefficients in K[x]. Typical examples are rational series like (1+x)^(-1) or roots of polynomials like sqrt(1+x). In characteristic 0, it is an open problem to characterize the...

From Brauer trees to surface algebras
Speaker: Karin Erdmann (Univ. of Oxford, UK)
We describe algebras constructed from graphs, and from surface triangulations, starting with Brauer tree algebras. We discuss how J. A. Green's walk around the Brauer tree generalizes....

The category of Brouwer operations: a basis for an understanding of choice sequences
Speaker: Martin Hyland (Univ. of Cambridge, UK)
Intuitionism as first proposed by the Dutch mathematician L. E. J. Brouwer involved not simply the well-known refusal of the law of the excluded middle but a notion, that of free choice sequence which is prima facie incompatible with classical mathematics. The theory of choice sequences uses...

2-Representations of dihedral and trihedral Soergel bimodules
Speaker: Marco Mackaay (Univ. Algarve)
2-Representation theory of monoidal categories is the categorical analogue of representation theory of algebras. In my talk, I will discuss the 2-representation theory of (sub)-quotients of the monoidal categories of Soergel bimodules of affine type A1 and A2, which are closely related to...

Nonparametric first-order analysis of spatial and spatio-temporal point processes. Application to wildfire patterns
Speaker: Wenceslao González Manteiga (Univ. Santiago de Compostela, Spain)
Spatial point patterns arise in a wide variety of scientific contexts, including seismology, forestry, geography and epidemiology. Wildfire is the most ubiquitous natural disturbance in the world and represents a problem of considerable social and environmental importance; particularly, in...

Quantum chaology in phase space through the Wigner transform
Speaker: Luís Pereira (Univ. Lisboa)
The Wigner function is one of the five major equivalent formulations of Quantum Mechanics. The others being Schrödinger's Heisenberg's, Feynman's path integral and the Density Operator. The study of the quantization of classically chaotic systems in the 70's led to the generalization of...

Totalitarian random Tug-of-War games and Jensen's extremal equations
Speaker: Fernando Charro (CMUC)
See the attached file.   ...

Some results on stochastic ageing and ordering
Speaker: Idir Arab (CMUC, Univ. Coimbra)
The concepts of stochastic ageing and ordering, which play an important role in any reliability analysis, describe how a component or system improves or deteriorates with age, and how to decide which component or system is ageing faster (in some sense). Stochastic ordering of distributions...

Right-angled Artin groups: commensurability classification and subgroup intersection problem
Speaker: Alexander Zakharov (CMUP, Univ. Porto)
The class of right-angled Artin groups (RAAGs) is a prominent class of groups which is widely studied in different branches of mathematics and computer science. Two groups are called commensurable if they have isomorphic subgroups of finite index. In the first part of the talk I will present...

Jacobi structures with a non-exact twist
Speaker: Cornelia Vizman (West Univ. Timisoara, Romania)
We introduce a concept of twisted Jacobi structure that extends the twisted Jacobi structure of Petalidou and Nunes da Costa, as well as the twisted Poisson structure in wide sense (i.e. with an arbitrary 3-form).​W​e ​explain the​ one-to-one correspondence between...

The Kostant form of \(\mathfrak U(sl^+_n)\) and the Borel-Schur algebra
Speaker: Ana Paula Santana (CMUC, Univ. Coimbra)
See the attached file...

The number of parking functions with center of a given length
Speaker: Rui Duarte (Univ. Aveiro)
Let 1\leq r\leq n and suppose that, when the Depth-first Search Algorithm is applied to a given rooted labelled tree on n+1 vertices, exactly r vertices are visited before backtracking. Let R be the set of trees with this property. We count the number of elements of R.For this purpose, we...

Characterization of interpolation between Grand, small or classical Lebesgue spaces
Speaker: Amiran Gogatishvili (Czech Academy of Sciences, Prague, Czech Republic)
See the attached file....

Some results on dependent random variables
Speaker: Milto Hadjikyriakou (Univ. of Central Lancashire, Cyprus)
In recent years, concepts of dependence have been the focus of substantial research activity and applications of dependent random variables can be found in many different fields. In the first part of this talk some classes of dependent random objects are presented together with various...

Continuous weak selections on compact-like spaces
Speaker: Tsugunori Nogura (Ehime Univ., Japan)
See attached file....

Regularity of interfaces for a Pucci type segregation problem
Speaker: Verónica Quítalo (CMUC, Univ. Coimbra)
In this talk we will start giving a brief review about a segregation model with nonlinear diffusion that evolve to a free boundary problem as a motivation for our problem. Then we will present our latest results for the regularity of the limit solution as well as the regularity of the free...

On the combinatorics of a family of generalized Catalan triangles
Speaker: Angela Mestre (Univ. Lisboa)
We generalize Aigner's array of the ballot numbers to a family of Riordan arrays. The entries of these generalized Catalan triangles are homogeneous polynomials in two variables which interpolate between the ballot numbers and the binomial coefficients. We show that the generalized Pascal...

Time-analyticity of fluid particle trajectories in ideal fluid flow
Speaker: Vladislav Zheligovsky (Russian Academy of Sciences)
In his 1815 manuscript, Cauchy showed that the equations governing the motion of particles in ideal fluid flow can be once integrated in time. This yields what is now known as the Cauchy invariants. The invariants are then used to derive recurrence relations for the time-Taylor coefficients...

The faceless problem
Speaker: F. J. García-Pacheco (Univ. Cadiz, Spain)
Internal points were introduced in the literature of topological vector spaces to characterize the nest locally convex vector topology. Later on, they have been generalized to the context of real vector spaces by means of the inner points. Inner points can be seen as the most opposite...

First-order, stationary mean-field games with congestion
Speaker: Levon Nurbekyan (KAUST, Saudi Arabia)
Mean-field games (MFGs) are models for large populations of competing, rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas. In this talk, I will present a recent contribution...

On the representation theory of the Infinite Unitriangular group
Speaker: Jocelyn Lochon (Univ. Lisboa)
Let U(q) denote the set of infinite nilpotent matrices over the finite field with q elements, called infinite unitriangular group. It is a wild group (not type I), thus the irreducible representation do not admit any reasonable parametrization.Nevertheless the set of all characters...

Integers and ideals: there and back again
Speaker: Peter Lombaers (UC|UP PhD student)
In number theory, when you try to solve an equation in a number field, it is often more convenient to work with ideals than with integers. This stems from the fact that ideals have unique factorization, but integers may not. I will explain the advantages and difficulties of this method...

Introducing (T,V) -categories
Speaker: Willian Silva (UC|UP PhD student)
In this seminar we introduce the concept of (T,V)-categories through its fundamental examples. In order to do so, we explore the concepts of monads and quantales, also with examples. We finish relating to the work on cartesian closed categories. The seminar takes place in...

SOS versus SDSOS polynomial optimization
Speaker: Mina Saee Bostanabad (UC|UP PhD student)
It is NP-hard to decide whether a polynomial is nonnegative, however, semidefinite programming can be used to decide whether a polynomial is a sum of squares of polynomials (SOS) in a practically efficient manner. In the context of polynomial optimization, it has become usual to substitute...

Inverse monoids and immersions of cell complexes
Speaker: Nora Szakács (CMUP, Univ. Porto)
In the talk, we study immersions between cell complexes using inverse monoids. By an immersion f : D -> C between cell complexes, we mean a continous map which is a local homeomorphism onto its image, and we further suppose that commutes with the characteristic maps of the cell complexes....

Deformations of coisotropic submanifolds in Jacobi manifolds
Speaker: Alfonso Tortorella (CMUC, Univ. Coimbra)
Originally introduced by Kirillov and Lichnerowicz, Jacobi manifolds encompass, unifying and generalizing, locally conformal symplectic/Poisson manifolds and (non-necessarily coorientable) contact manifolds. In this talk, in order to investigate the coisotropic deformation problem, we attach...

Oscillatory and nonoscillatory behavior of a differential delay system of order n
Speaker: Sandra Pinelas (Academia Militar)
See file attached...

Embeddings of weighted Morrey spaces
Speaker: Dorothee Haroske (Univ. Jena, Germany)
See the attached file...

Lagrangian controllability for the 3D Navier-Stokes equations
Speaker: Vahagn Nersesyan (Univ. Versailles, France)
In the Eulerian approach, the motion of an incompressible fluid is usually described by the velocity field which is given by the Navier-Stokes system. The velocity field generates a flow in the space of volume-preserving diffeomorphisms. The latter plays a central role in the Lagrangian...

Joins of closed sublocales, coframes of sublocales, and frames of sublocales
Speaker: Aleš Pultr (Charles Univ., Prague, Czech Republic)
Topics to be covered: 1. The frame Sc(L) of joins of closed sublocales of a locale L; motivation (scatteredness). 2. The relation of Sc(L) to the coframe of sublocales S(L). 3. Sc(L) as a "discrete cover" of L, modelling discontinuity. 4. Comparing Sc(L) with the frame of...

Towards a pseudoequational proof theory
Speaker: Jorge Almeida (CMUP, Univ. Porto)
A new scheme for proving pseudoidentities from a given set Σ of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when Σ defines a locally finite variety, a pseudovariety of groups or, more generally, of completely simple...

Variational obstacle avoidance problem on Riemannian manifolds
Speaker: Margarida Camarinha (CMUC, Universidade de Coimbra)
Motion planning with obstacle avoidance is an important task in the field of robotics. Many methods for autonomous vehicle navigation with obstacle avoidance have been developed in the last few decades. I will talk about a variational obstacle avoidance problem on a Riemannian manifold and...

A new signature of quantum phase transitions from the numerical range
Speaker: Stephan Weis (Université libre de Bruxelles, Belgium)
A quantum phase transition is a ground state phenomenon in an infinite lattice model with various defining key properties. We focus on two of them and point out their signatures in finite lattice models: Non-analyticity of the ground state energy and strong variation of the entropy of...

Overlapping domain decomposition algorithms for singularly perturbed parabolic problems
Speaker: Sunil Kumar (Indian Institute of Technology, India)
in the attached file...

On the Kantor product
Speaker: Ivan Kaygorodov (Univ. Federal do ABC, Santo André, Brazil; Siberian State Aerospace Univ., Krasnoyarsk, Russia)
Kantor defined the conservative algebras as an generalization of Lie and Jordan algebras. There are many relations between conservative algebras and other non-associative algebras. We will talk about some classical papers of Kantor and some new results obtained in some joint work with Yu....

On a quadratic Schrödinger system
Speaker: Filipe Oliveira (Univ. Nova de Lisboa)
See the attached file...

Nonorientable hypermaps
Speaker: Daniel Marques Pinto (CMUC, University of Coimbra)
Topologically, a hypermap is a cellular embedding of a connected hypergraph into a closed connected surface. If that underlying surface is orientable, we say that the hypermap is orientable. Otherwise, the hypermap is called nonorientable. We will present some results about nonorientable...

Radial and block-radial subspaces of Sobolev and Besov spaces: regularity, decay and compactness
Speaker: Leszek Skrzypczak (Adam Mickiewicz Univ., Poznan, Poland)
See the attached file...

Analytical and numerical methods for a class of second and third kind Volterra integral equations
Speaker: Sonia Seyed Allaei (CMUC)
See the attached file. ...

Two mathematical approaches in ophthalmology
Speaker: Maryam Khaksar Ghalati
TBA Maryam Khaksar Ghalati is a former PhD student of the Joint PhD Program UC|UP, in the area "Numerical Analysis andOptimization" under the supervision of professors Adérito Araújo and Sílvia Barbeiro. ...

Reducibility of nilpotent cone for G-Higgs bundle moduli space
Speaker: Azizeh Nozad (Univ. Lisboa)
TBA Azizeh Nozad is a Postdoctoral fellow at Faculty of Science, University of Lisbon....

Statistical instability for the contracting Lorenz flow
Speaker: Muhammad Ali Khan (UP student)
TBA Muhammad Ali Khan is a PhD student of the Joint PhD Program UC|UP, working at the University of Porto, in the areaof "Dynamical Systems" under the supervision of professor José Ferreira Alves.  ...

Semisimple Hopf actions and factorization through group actions
Speaker: Deividi Pansera (Univ. Porto)
See the attached file....

Singularities of non-commutative integrable systems
Speaker: Rui Loja Fernandes (Univ. of Illinois at Urbana-Champaign, USA)
Integrable systems that appear in "nature" always have singularities and there is a well-known theory of non-degenerate singularities, which are divided into 3 classes: elliptic, focus-focus and hyperbolic classes. However, in the case of non-commutative integrable systems, such a...

On Besov spaces of smoothness zero
Speaker: Oscar Domínguez (CMUC)
see the attached file...

Extensions of Herstein's theory on Jordan (and Lie structures) to more general associative systems
Speaker: Fernando Montaner (Univ. Zaragoza, Spain)
In the mid 1950s Herstein's opened a field of research which had as its aim the study of the structures of Lie and Jordan algebras that can be obtained from an associative algebra (possibly, with an involution) by endowing it with the Lie product ([xy]=xy-yx) or the Jordan product...

Early exercise boundaries for American-style knock-out options
Speaker: José Carlos Dias (ISCTE-IUL Business School)
Under mild assumptions, this paper proposes a novel representation for the early exercise boundary of American-style double knock-out options in terms of the simpler optimal stopping boundary of a nested single barrier American-style contract. Therefore, and from now on, any single-factor...

Characterization and estimation of the upcrossings index

Ana Paula Martins (CMA-UBI, Univ. da Beira Interior)

Extreme Value Theory aims to predict occurrence of rare events, which in numerous situations have disastrous impacts, making an adequate estimation of the parameters related with such events of primordial importance in Statistics of Extremes. The extremal index and the upcrossings index play...

Combinatorics and HOMFLYPT invariants of knots
Speaker: Marko Stosic (IST, Lisboa)
HOMFLYPT invariants are one of the most important and general invariants in the study of the topological properties of knots. Apart from the purely knot-theoretic interest, they are related to numerous different areas of mathematics and physics, including representation theory, operator...

On a generalized nonlinear heat equation in Besov and Triebel-Lizorkin spaces
Speaker: Franka Baaske (Friedrich-Schiller-Univ. Jena, Germany)
See the attached file...

The \(\theta\)-parareal schemes
Speaker: Richard Tsai (Univ. of Texas at Austin, USA)
We propose a variant of the parareal method for parallel-in-time computation of time dependent problems. We call it the θ-parareal schemes because it formally resembles the θ-schemes for discretizing time dependent partial differential equations. We analyze the linear stability of...

Morrey spaces on domains: different approaches and growth envelopes
Speaker: Cornelia Schneider (Univ. Erlangen-Nuremberg, Germany)
see the attached file...

Corecursive algebras
Speaker: Jiří Adámek (Tech. Univ. Braunschweig, Germany)
There are various models of algebras in which certain recursive equations are uniquely solvable. A simple one was introduced by Capretta, Uustalu and Vene: given an endofunctor H, recursive equations are formalized as coalgebras for H. An algebra for H is called corecursive if every...

Polytopes, slack ideals and psd-minimality
Speaker: João Gouveia (CMUC / Univ. Coimbra)
The slack ideal is an algebraic object that codifies the geometry of a polytope. This notion was motivated by the study of psd-minimality of polytopes: A d-polytope is said to be psd-minimal if it can be written as a projection of a slice of the cone of d+1 by d+1 positive semidefinite...

A symbolic approach to perturbed second degree forms: study of the case of perturbed Chebyshev polynomials
Speaker: Zélia Rocha (CMUP, Univ. Porto)
See the attached file....

Graph complexes and configuration spaces of points
Speaker: Ricardo Campos (ETH Zürich, Switzerland)
Given a manifold M, one can study the configuration space of n points on the manifold, which is the subspace of M^n in which two points cannot be in the same position. The study of these spaces from a homotopical perspective is of interest in very distinct areas such as algebraic topology or...

An introduction to \(L_\infty\) algebras and \(L_\infty\) algebroids
Speaker: Raquel Caseiro (CMUC/Univ. Coimbra)
\( L_\infty \) algebras are natural generalizations of Lie algebras from a homotopy theoretical point of view. The original definition dates back to 1992 by J. Stasheff and T. Lada and the idea is to weaken the condition imposing that the Lie bracket satisfies the Jacobi identity. Instead...

How to extend an edge colouring?
Speaker: António Girão (Univ. Cambridge, UK)
See attached pdf file....

Fast algorithms for high frequency wave propagation
Speaker: Bjorn Engquist (Univ. of Texas at Austin, USA)
Direct numerical approximation of high frequency wave propagation typically requires a very large number of unknowns and is computationally very costly. We will discuss two aspects of this type of problem. One is the development and analysis of fast algorithms...

Magnitude homology
Speaker: Tom Leinster (Univ. of Edinburgh, UK)
Magnitude homology is a homology theory of enriched categories, proposed by Michael Shulman late last year. For ordinary categories, it is the usualhomology of a category (or equivalently, of its classifying space). But for metric spaces, regarded as enriched categories à la...

General monotonicity concept and its applications
Speaker: Sergey Tikhonov (CRM, Barcelona, Spain)

Volterra integral equations for non linear partial differential equations of integrable type
Speaker: Luisa Fermo (Univ. of Cagliari, Italy)
Nonlinear partial differential equations (NPDE) of integrable type have important physical applications. They are used to describe electromagnetic waves in optical fibers, surface wave dynamics, charge density waves, breaking wave dynamics etc. Their corresponding initial value problem (IVP)...

Optimal transport, PDEs and geometry
Speaker: Dmitry Vorotnikov (CMUC, Univ. Coimbra)
Various nonlinear evolutionary partial differential equations (coming from physics, fluid and solid mechanics, biology, chemistry etc.) can be viewed as geodesic equations or gradient flows on infinite-dimensional Riemannian structures.Understanding the underlying geometry of a PDE...

Combinatorics in minimal case completions of matrix pencils
Speaker: Marija Dodig (Univ. Lisboa)
In this talk we shall present some combinatorial tools in resolving matrix pencil completion problems. Also, we shall explain the concept of minimal completions, and present the solution of the general matrix pencil completion problem in the minimal case....

Solution of a matrix problem coming from differential equations
Speaker: Charles R. Johnson (College of William and Mary, Williamsburg, USA)

Resolvability of topological spaces
Speaker: István Juhász (Alfréd Renyi Inst. of Mathematics, Budapest, Hungary)
A topological space X is called λ-resolvable, where λ is a (finite or infinite) cardinal, if X contains λ many pairwise disjoint dense subsets. X is maximally resolvable if it is ∆(X)-resolvable, where ∆(X) = min{|G| : G open, G =/= ∅} .The...

Hopf algebras and Ore extensions
Speaker: Christian Lomp (Univ. Porto)
Enveloping algebras of Lie algebras are typical examples of Hopf algebras. Some of them can be presented as iterated Ore extensions, which are a sort of non-commutative polynomial rings. This raises the natural question as to which Ore extensions over a Hopf algebras R admit a Hopf algebra...

An introduction to Sasakian manifolds
Speaker: Antonio de Nicola (CMUC, Univ. Coimbra)
I will introduce the first elements of contact and almost contact geometry, starting from the notion of contact manifold. I will briefly mention its relation with symplectic geometry as well as some application to physics. I will present the notions of normality and compatible metric in an...

Renormalized transport of inertial particles
Speaker: Marco Martins Afonso (CMUP, Univ. Porto)
We study how an imposed fluid flow - laminar or turbulent - modifies the transport properties of inertial particles, namely their terminal velocity, effective diffusivity, and concentration following a point-source emission.Such quantities are investigated by means of analytical and...

Nonparametric models for extreme risks with urn models
Speaker: Juerg Husler (Univ. of Bern, Switzerland)
Extreme risk is often modelled with parametric or semi-parametric models. Here we present nonparametric models for a large setup of risks where the underlying process is not stationary, but is changing with time. The approach is based on the flexible class of urn models. This is made...

On some categorical-algebraic conditions in S-protomodular categories
Speaker: Andrea Montoli (Università degli Studi di Milano, Italy)
We study, in the context of S-protomodular categories, relative versions of some categorical-algebraic conditions already considered for semi-abelian categories, like the algebraic coherence and the local algebraic cartesian closedness. The goal is to obtain a hierarchy between...

Interesting algebras between Kleisli and Eilenberg-Moore
Speaker: Lurdes Sousa (CMUC, IP Viseu)
We investigate important categories lying strictly between the Kleisli category and the Eilenberg-Moore category, for a Kock-Zöberlein monad on an order-enriched category. The situation is dramatically different from the particular case of idempotent monads, for which there are no...

Characterization of Sobolev spaces through functionals without derivatives dependence
Speaker: Ana Margarida Ribeiro (CMA, Univ. Nova de Lisboa)
Extending previous works due to Bourgain, Brézis, and Mironescu [J. Anal. Math. 87 (2002)] and Leoni and Spector [J. Funct. Anal. 261, 10 (2011)], we provide new characterizations of Sobolev spaces in terms of functionals involving difference quotients. These characterizations have...

Connection techniques for the study of the structure of algebraic objects
Speaker: José M. Sánchez (CMUC)
After recalling classical results in order to place our work, we summarize the evolution of the connection techniques and its useful applications to the study of split decompositions. By making use of these techniques, we focus our attention on the study of the structure and the simplicity...

On the construction of complex algebraic surfaces
Speaker: Carlos Rito (CMUP, Univ. Porto)
Surfaces of general type are far from being classified. Frequently the construction of a single example is a challenge, even for the ones with low values of the invariants. The most efficient methods of construction are classical: quotients by the action of a group and coverings. In this...

Extremal behavior of chaotic dynamical systems
Speaker: Ana Cristina Moreira Freitas (CMUP, Univ. Porto)
This talk is about the study of rare events for chaotic dynamical systems.We will address this issue by two approaches. One regards the existence of Extreme Value Laws (EVL) for stochastic processes obtained from dynamical systems, by evaluating an observable function (which achieves a...

On a regularity conjecture for degenerate elliptic pdes
Speaker: José Miguel Urbano (CMUC, Univ. Coimbra)
We establish a new oscillation estimate for solutions of nonlinear partial differential equations of degenerate elliptic type, which yields a precise control on the growth rate of solutions near their set of critical points. We then apply this new tool in the investigation of a longstanding...

Non Fickian diffusion in porous media
Speaker: José Augusto Ferreira (CMUC, Univ. Coimbra)
Transport processes in porous media have being described by the classical convection-diffusion equation for the concentration coupled with an elliptic equation for the pressure and Darcy’s law for the velocity. Despite the popularity of this model, gaps between experimental data...

Paths to uniqueness of critical points and applications
Speaker: Hugo Tavares (U. Lisboa)
In this talk we show a unified and general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our method relies on convexity properties along suitable paths. To illustrate our method we present a...

Constrained partitions in graphs: bio and financial applications
Speaker: Pedro Martins (IPCoimbra and CMAF-CIO)
This seminar addresses partition problems in graphs, from an applied perspective. We discuss results and formulations, ranging from very restrictive partition components (partition into cliques) to less restrictive ones (partition into trees - a forest). We also compare these results with...

O Naufrágio da Namíbia. Um Espólio Bem Guardado
Speaker: José Malhão Pereira (Academia de Marinha e Centro de História das Ciências da UL)
Na manhã do dia 1 de Abril de 2008, pessoal da empresa Namdeb da Namíbia, removendo a areia junto à costa a cerca de 18 quilómetros da foz do rio Orange, que faz a fronteira com a África do Sul, encontraram madeira, lingotes de cobre e duas peças de...

The deformation cohomology of a Lie groupoid and applications to rigidity
Speaker: João Nuno Mestre (CMUC/Univ. Coimbra)
In this talk we discuss deformations of Lie groupoids and introduce the cohomology which controls them. We then study some of its properties, and give a geometric interpretation for it in low degrees. We will also look at relations with other cohomologies: deformation cohomologies for...

Optimal simplex finite-element approximations of arbitrary order in curved domains circumventing the isoparametric technique
Speaker: Vitoriano Ruas (Univ. Pierre et Marie Curie, Paris, and Catholic Univ., Rio de Janeiro)
One of the reasons for the undeniable success of the finite-element method in the applied sicences is its great versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In this case method's isoparametric...

The combinatorics of noncrossing and nonnesting partitions
Speaker: Ricardo Mamede (CMUC, Univ. Coimbra)
After a brief introduction to abstract Coxeter systems using a combinatorial approach based on words, we discuss recent developments on two combinatorial objects associated to the classical Coxeter groups: noncrossing and nonnesting partitions....

On the representation theory of some Noetherian algebras
Speaker: Paula Carvalho (CMUP, Univ. Porto)
I will present some classes of Noetherian algebras that I have been studying regarding their representation theory; down-up algebras and skew polynomial rings, presenting past and present results. If time allows, another class of algebras will be introduced for which it is unknown when they...

Approximation in Morrey spaces
Speaker: Alexandre Almeida (Univ. Aveiro)
We introduce a new subspace of Morrey spaces where the approximation by nice functions is possible in Morrey norm. In particular, we obtain an explicit description of the closure of the set of all infinitely differentiable compactly supported functions in Morrey spaces....

Dual enrichment and Isbell Duality
Speaker: Martin Hyland (Univ. of Cambridge, UK)
The category of presheaves on a given small category is enriched in the category of presheaves on its opposite. This piece of Category Theory folklore is under appreciated perhaps because it is not clear what to do with it. I shall discuss versions of this phenomenon and how it looks from...

Sign patterns of coefficients of power series associated with the spectra of positive matrices
Speaker: Thomas Laffey (Univ. College Dublin, Ireland)
See attached pdf file....

Statistical detection of some topological and geometric features
Speaker: Antonio Cuevas (Univ. Autónoma de Madrid, Spain)
The subject of this talk is closely related to the theories of set estimation and manifold estimation. Our object of interest is a, possibly lower-dimensional, compact set M in Rd. The general aim is to identify (via stochastic procedures) some qualitative or quantitative features of M of...

Multiple orthogonal polynomials and some of their applications
Speaker: Walter Van Assche (KU Leuven, Belgium)
Multiple orthogonal polynomials are polynomials in one variable that satisfy orthogonality conditions with respect to several measures. I will briefly give some general properties of these polynomials (recurrence relation, zeros etc.). These polynomials have recently appeared in many...

A geometric glimpse to certain classes of first order PDE's
Speaker: Franco Magri (Univ. degli Studi di Milano-Bicocca, Italy)
The purpose of the talk is to illustrate , on a simple example, how ideas from the theory of singularities, from the theory of Riemannian and Frobenius manifolds, and from Hamiltonian mechanics beautifully intertwine in the study of certain classes of first order PDE's of hydrodynamic...

Internal Schensted insertion and tableau-switching involution
Speaker: Olga Azenhas (CMUC, Univ. Coimbra)
Robinson-Schensted insertion and Sch\"utzenberger jeu de taquin are central operations in algebraic combinatorics with deep applications in other areas. Knuth transformations on words explain how they are related by showing what they do on words. This allows to replace insertion...

On ARL-unbiased c-charts for INAR(1) Poisson counts
Speaker: Manuel Cabral Morais (CEMAT, Univ. Lisboa)
Counts of nonconformities are frequently assumed to have a Poisson distribution. The integer and asymmetrical character of this distribution and the value of its target mean may prevent the quality control operator to deal with a chart with a pre-specified in-control average run length (ARL)...

The ADR algebra and other strongly quasihereditary algebras
Speaker: Teresa Conde (Univ. Stuttgart, Germany)
Quasihereditary algebras were introduced by Cline, Parshall and Scott in order to deal with highest weight categories arising from Lie theory. A prototype for quasihereditary algebras are the Schur algebras.Given a finite-dimensional algebra A, we may associate to it a special endomorphism...

Some tools for the study of Cartan connections on proper Lie groupoids
Speaker: Giorgio Trentinaglia (IST, Lisboa)
I will describe some results of mine suggesting a clear strategy for the study of the following basic questions - about which little seems to be known - concerning Cartan (i.e. multiplicative) connections on proper Lie groupoids: a) What are the obstructions to the existence of Cartan...

Castelnuovo-Mumford regularity and graph invariants
Speaker: Jorge Neves (CMUC, Univ. Coimbra)
The work of R. Stanley exposed a strong link between the theory of ideals of a polynomial ring generated by monomials and the theory of simplicial complexes. Recently, other bridges have been established between combinatorial structures and classes of ideals not necessarily generated by...

Systems of partial differential equations arising from population dynamics and neuroscience: Free boundary problems as a result of segregation
Speaker: Verónica Quítalo (Univ. Coimbra - CoLab UT Austin Portugal Program)
In this talk we will present some two phase free boundary problems arising from population dynamics. We will focus on systems with fully nonlinear diffusion and local interaction, and linear systems with a (non local) long range interaction. In the long range model, the growth of a...

Derivations and generalized derivations of non-associative algebras
Speaker: Ivan Kaygorodov (Univ. Federal do ABC, Brazil)
A famous theorem of Jacobson talks about the nilpotency of any finite dimensional Lie algebra with an invertible derivation. We will discuss about some generalizations of this theorem for the case of Leibniz derivations and other non-associative algebras. In particular, we will talk about...

How to centralize and normalize quandle extensions
Speaker: Mathieu Duckerts-Antoine (CMUC)
During this talk, we will study different classes of quandle homomorphisms defined with respect to a fundamental reflection of the category of quandles into its full subcategory of trivial quandles. I will recall the notion of a central extension and of a normal extension coming from...

A short survey on Copositive and Completely Positive optimization

Paula Amaral (Univ. Nova de Lisboa)


Copositive (Cop) and Completely Positive (ComP) Optimization is a recent and growing area of research. It has shown that several NP-hard optimization problems can be expressed as Cop or Comp programs, linear programs over the convex cone of copositive or completely positive matrices.In this...

Geometric regularity theory for fully nonlinear elliptic equations
Speaker: Edgard A. Pimentel (Univ. São Carlos, Brazil)
In this talk, we examine the regularity theory for fully nonlinear elliptic equations of the form F(D^2 u)=f(x) where F is a (λ,Λ)-elliptic operator and f:B1→ℝ is a continuous source term, in appropriate Lebesgue spaces. We recur to a set of tools known as geometric-...

Finite dimensional Poisson algebras
Speaker: Mohamed Boucetta (Univ. Cadi-Ayyad, Marrakech, Morocco)
See attached file. ...

On locally conformal symplectic manifolds of the first kind
Speaker: Juan Carlos Marrero (Univ. of La Laguna, Tenerife, Spain)
In this talk, I will present some recent results on locally conformal symplectic manifolds of the first kind. In fact, under certain topological restrictions related with the compactness of the canonical foliation, we will discus a structure theorem for these manifolds. In the non compact...

On Taken's Last Problem: times averages for heteroclinic attractors
Speaker: Alexandre A. Rodrigues (CMUP, Univ. Porto)
In this talk, after giving a technical overview about the topic, I will discuss some properties of a robust family of smooth ordinary differential equations exhibiting tangencies for a dense subset of parameters. We use this to find dense subsets of parameter values such that the set of...

Singularities of vector fields and the dimension of groups of holomorphic diffeomorphisms
Speaker: Helena Reis (CMUP, Univ. Porto)
The group of holomorphic diffeomorphisms, Aut(M), of a compact complex manifold M is a Lie group of finite dimension. To provide bounds for the dimension of these groups is a classical problem in complex analysis. It is well known that the dimension of Aut(M) cannot be bounded in terms of...

Topological mirror symmetry for parabolic Higgs bundles
Speaker: André Oliveira (CMUP, Univ. Porto)
See attached file....

The C^{p'}-regularity conjecture in the plane
Speaker: Damião Araújo (UNILAB and UFPB, Brazil)
We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are...

Extreme supercharacters of the infinite unitriangular group
Speaker: Carlos André (CEAFEL, Univ. Lisboa)
We define extreme supercharacters of the infinite unitriangular group, introduce the ramification scheme associated with the classical supercharacter theories of the finite unitriangular groups and describe how extreme supercharacters of the infinite unitriangular group appear as weak limits...

Smoothness Morrey spaces and their envelopes
Speaker: Susana Moura (CMUC, Univ. Coimbra)
See attached file....

A meeting between Sobolev, Bessel, Hölder, Lorentz and Karamata in order to discuss optimal embeddings and some open problems
Speaker: Júlio Neves (CMUC, Univ. Coimbra)
In this talk we give a short survey on the results of embeddings of Sobolev type spaces into Hölder type spaces, including as well the famous result of Brézis and Wainger about almost Lipschitz continuity of elements of the Sobolev space with super-critical exponent of...

Monoidal categorical Galois theory
Speaker: Dimitri Chikhladze (CMUC, Univ. Coimbra)
In this talk I will explain a generalization of the categorical Galois theory of Janelidze to a context of monoidal category theory, and its relationship with the work of Deligne on Tannakian categories....

Equidivisible pseudovarieties of semigroups
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
A semigroup is said to be equidivisible if distinct factorizations of an element have always a common refinement. Groups and free semigroups are examples of equidivisible semigroups.We give a complete characterization of pseudovarieties of semigroups whose finitely generated relatively free...

The p-median on disconnected graphs
Speaker: Jorge Orestes Cerdeira (Univ. Nova de Lisboa)
The <i>p</i>-median problem is a well-known NP-hard combinatorial optimization problem that seeks for the location of p facilities on the vertices (customers) of a graph G to minimize the sum of transportation costs for satisfying the demands of the customers from the...

The embeddings of Jawerth and Franke for Besov and Triebel-Lizorkin spaces with variable exponents
Speaker: Helena Gonçalves (Technische Univ. Chemnitz, Germany)
See the attached file...

A successful pair: symbolic dynamics and (pro)finite semigroups
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
My research has been mostly about exploring natural links between the field of symbolic dynamics and the theory of finite and profinite semigroups, with applications in both directions. The aim of this talk is to give examples of relevant results and open problems stemming from this line of...

Ring theoretical and combinatorial aspects of representation theory
Speaker: Samuel Lopes (CMUP, Univ. Porto)
I will discuss some of my research interests in relation to representation theory of infinite dimensional algebras, highlighting the interplay with topics in ring theory and combinatorics....

Diverse paths in network optimisation
Speaker: Marta Pascoal (Univ. Coimbra)
A path in a graph is a sequence of vertices linked by graph edges. The determination of an optimal path with respect to a given objective function has led to classical network optimization problems. However, for many applications, it is useful to know an alternative backup solution,which can...

Positive semidefinite rank and representations of polytopes
Speaker: João Gouveia (CMUC, Univ. Coimbra)
Let M be a p-by-q matrix with nonnegative entries. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices A_i,B_j of size k×k such that M_{ij}=trace(A_i,B_j). The psd rank was recently introduced, and has has ...

Transverse measures and densities for Lie groupoids
Speaker: João Nuno Mestre (CMUC, Univ. Coimbra)
We explain how extending Haefliger's approach to transverse measures for foliations to general Lie groupoids allows us to define and study measures and geometric measures (densities) on differentiable stacks. The abstract theory works for any differentiable stack, but it becomes very...

The deficiency of categories
Speaker: Fernando Lucatelli Nunes (CMUC)
The study of the deficiency of a category arises from the problem of understanding what is a presentation of a category with the least number of equations and, therefore, avoiding redundancy.I have been studying deficiency within the context of descent and lifting of biadjoints (within the...

Implementing a stable version of the tau method in a toolbox
Speaker: José Matos (ISEP)
The Lanczos' tau method is a spectral method originally proposed to solve linear differential problems with polynomial coefficients. Generalizations to extending its domain of application to integro-differential, nonlinear and functional-differential problems, among others, have been made....

Explicit Schoen Surfaces
Speaker: Carlos Rito (Centro de Matemática da Universidade do Porto)
See the attached file....

Group theory and special functions theory: a two way street
Speaker: R. Álvarez-Nodarse (Univ. Sevilla, Spain)
It is well known the role of symmetries in Science and, particular, in the Physical Sciences. Almost all physical laws are consequence of symmetries. Take as an example the conservation laws of Classical Mechanics and the Noether's theorem. Another interesting example is related to...

Reconstruction of complex-valued once differentiable conductivities in 2D
Speaker: Evgeny Lakshtanov (Univ. Aveiro)
The classical dbar-method has been generalized recently by Lakshtanov, Novikov, Vainberg to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem without assumptions on smoothness of potentials. As a consequence, this provides...

A fractional diffusion model with resetting
Speaker: Ercília Sousa (CMUC, Univ. Coimbra)
We consider a fractional partial differential equation that describes the diffusive motion of a particle, performing a random walk with Lévy distributed jump lengths, on one dimension with an initial position x0. The particle is additionally subject to a resetting dynamics, whereby...

Image processing using nonlinear partial differential equations
Speaker: Sílvia Barbeiro (CMUC, Univ. Coimbra)
When assigned with the task of image reconstruction, the first challenge one faces is the derivation of a truthful model for both the information we want to extract and the data. The natural question arises: how can we make our model adaptive to the given data? Diffusion processes are...

The extension operator in variable exponent function spaces
Speaker: Henning Kempka (Technische Univ. Chemnitz, Germany)
The abstract is in the attached pdf file...

First degree cohomology of Specht modules and extensions of symmetric powers
Speaker: Stephen Donkin (Univ. of York, UK)
This is joint work with H. Geranios. We compute the dimensions of the first degree cohomology of all Specht modules for symmetric groups in characteristic different from 2. Our method is to make a comparison with extension groups for general linear groups and Borel subgroups and then make a...

Stochastic dynamics on point processes
Speaker: Antonio Sodre (Department of Mathematics, Univ. of Texas at Austin)
Deterministic dynamics on stationary point process in R^d are built upon compatible point-shifts:  translation invariant mappings from each point of the process to another. When a point-shift is applied multiple times to a point-process it creates a sequence of distributions, namely,...

Saturated numerical semigroups
Speaker: Manuel B. Branco (Univ. Évora)
See the attached file....

The variable coefficients thin obstacle problem
Speaker: Wenhui Shi (CMUC)
See the attached file....

On a fractional Monge-Ampère operator
Speaker: Fernando Charro (UPC, Barcelona, Spain) 
See the attached file. ...

Conjecture of Alon-Tarsi
Speaker: Carlos Gamas (Univ. Coimbra)
See the attached file...

Monochromatic configurations in finite colorings of N
Speaker: Joel Moreira (Ohio State Univ., USA)
Is it possible to color the natural numbers with finitely many colors, so that whenever x and y are of the same color, their sum x+y has a different color? A 1916 theorem of I. Schur tells us that the answer is *no*. In other words, for any finite coloring of N, there exist x and y such that...

A preaction of the 0-Hecke monoid
Speaker: Ana Paula Santana (CMUC, Univ. Coimbra)
I will construct a preaction of the Hecke monoid on the category of rational modules for the quantum negative Borel subgroup of the quantum general linear group. I will also show that this preaction induces a preaction on the category of modules for the quantised Borel-Schur algebra. This...

Homotopy Excision
Speaker: Fernando Lucatelli Nunes (UC student)
Eilenberg and Steenrod proved that ordinary homology is characterized by five axioms. Later, Atiyah, Hirzebruch and Whitehead observed that there are other families of functors that satisfy the four "most important" axioms. They defined the so called "generalized homology...

Homological Algebra
Speaker: Artur de Araujo (UP student)
We will explain the basic concepts of Homological Algebra (Cech cohomology, injective/projective resolutions, derived functors,) and show why, useful as they are, they have shortcomings for a general theory of cohomology. Time allowing, we'll give a hint of why derived categories make up for...

Semigroup of endomorphisms of a vector space
Speaker: A. R. Rajan (Univ. Kerala, India)
The semigroup of endomorphisms of a finite dimensional vector space is an extensively studied object in semigroup theory. Often it is identified with the semigroup M_n(K) of n × n matrices over a field K. As a ring M_n(K) is a basic ring used in structure theory of rings. Hence the...

Cross-connections of balanced categories

P. G. Romeo (Cochin Univ., India)

In this talk I will explain what a balanced category is and show that the ideal categories of a concordant semigroup are balanced categories. I will also mention about the cross-connection of such categories.An extended abstract of the talk is attached herewith....

Application of the Kalman filter in the statistical modelling of time series
Speaker: Marco Costa (ESTGA & CIDMA, Univ. Aveiro)
The Kalman Filter (KF), initially submitted by the Hungarian Rudolf E. Kalman in the context of control problems, has been widely applied in statistical modelling of stochastic processes that allow a state space representation. The success of the KF is attributed to the optimal estimators...

On Laguerre-Hahn orthogonal polynomials of class one
Speaker: Maria das Neves Rebocho (Univ. Beira Interior & CMUC)
We study recurrences for Laguerre–Hahn orthogonal polynomials of class one. It is shown for some families of such Laguerre–Hahn polynomials that the coefficients of the three term recurrence relation satisfy some forms of discrete Painlevé equations, namely dPI and...

Geometric and numerical methods for optimal control of mechanical systems
Speaker: Leonardo Colombo (Univ. Michigan, USA)
Under some mild regularity conditions, optimal control problems can be understood as higher-order variational problems. The aim of this talk is to give a general overview on the use of techniques concerning Geometric Mechanics and Geometric Numerical Integration to solve optimal control...

Finite difference methods for the reaction-wave-diffusion equation with distributed order in time
Speaker: Magda Rebelo (CMA/UNL)

On the works of A. Markov and Stieltjes on monotonicity of zeros
Speaker: Kenier Castillo (CMUC)
We discuss, in this didactical talk, old and new results on the monotonicity of zeros of polynomials paying special attention to the flexibility and versatility of the works of A. Markov and Stieltjes on the subject....

Topological spaces as algebras
Speaker: Pier Giorgio Basile (UC PhD student)
Monads, or triples, and the algebras they define, proved to be very important in several fields of mathematics. For example, they allow us to see the algebraic nature owned by topological spaces. This fact, for what concerns compact Hausdorff spaces, is known since 1969 (see [4]). By...

The LEGO of localic maps
Speaker: Jorge Picado (CMUC, Univ. Coimbra)
Assembling a localic map f : L → M from localic maps fi : Si → M, i ∈ J, defined on closed resp. open sublocales (J finite in the closed case) follows the same rules as in the classical case. The corresponding classical facts immediately follow from the behavior of preimages...

Reflectivity and its logics
Speaker: Lurdes Sousa (CMUC, IP Viseu)
In previous joint work with  Jirí  Adámek and Manuela Sobral we presented a logic for finitary epimorphisms which can be seen as an extension of Birkhoff's equational logic. In subsequent papers joint with Jirí Adámek and Michel Hébert, we...

Sobolev spaces with power weights perturbed by slowly varying functions
Speaker: Therese Mieth (Friedrich-Schiller-Univ. Jena, Germany)
See the attached file...

A model for phase transitions with competing terms
Speaker: Margarida Baía (IST, Lisboa)
In this work we study, via $\Gamma$-convergence techniques, the asymptotic behaviour of a family of coupled singular perturbations of a non-convex functional of the type $$\int_\Omega f(u(x),\nabla u(x),\rho(x)) \, dx $$ as a variational model to address  two-phase transitions problems...

Invariants and Hochschild cohomology of rings of differential operators in one variable
Speaker: Samuel Lopes (Univ. Porto)
A polynomial h in the variable x determines the derivation h(d/dx) of the polynomial ring F[x] and, together with the multiplication by x operator, it generates a noncommutative algebra A_h whose elements can be written as differential operators on h(d/dx) with coefficients in F[x]. I will...

A discrete nonsymmetric variant of the Minkowski Convex Body Theorem
Speaker: Stanislav Kondratyev (CMUC)
In this talk we discuss a discrete version of the Minkowski Convex Body Theorem for convex integer polygons on the plane. The theorem states that given a sublattice of the integer lattice, any such polygon with sufficiently many vertices contains at least one point of the sublattice. An...

Nijenhuis deformation of Gerstenhaber algebra and Poisson Quasi-Nijenhuis algebroids
Speaker: Mohammad Jawad Azimi (CMUC/Univ. Coimbra)
The importance of Nijenhuis tensor on the Lie algebra of vector fields on a manifold is not only because of the Newlander-Nirenberg theorem, but also it appears in the study of Hamiltonian systems. The notion is known for some geometric structures such as Poisson manifolds, Courant...

Gradient estimates for the porous medium equation
Speaker: Juhana Siljander (Univ. Jyväskylä, Finland)
The sharp regularity of weak solutions to the porous medium equation is a long-standing open problem. The fundamental solution of the problem, the so called Barenblatt solution, is known to be C^{1/(m-1)}-Hölder continuous, and it is a natural question whether this is the worst possible...

Biology and Mathematics: a strategic alliance against cancer through new anti-tumoral therapies
Speaker: Emanuela Signori (Univ. Rome, Italy)
Cancer remains one of the leading causes of death globally, affecting both sexes equally with an estimated 12.7 million cases around the world. This number is expected to increase to 21million by 2030, despite several curative strategies are offered to the patients. Therefore, new and...

Mixed-Effect State Space models applied to environmental data: the discrimination of the Water Quality Monitoring Sites in River Vouga
Speaker: Magda Monteiro (ESTGA & CIDMA, Univ. Aveiro)
The surface water quality monitoring is an important concern of public organizations due to its relevance for public health. Statistical methods are taken as consistent and essential tools in the monitoring procedures in order to prevent and identify environmental problems. This work...

Numerical investigations of spatially segregation models
Speaker: Farid Bozorgnia (IST, Univ. Lisboa)
In this talk, we consider different models of Reaction-Diffusion system which describe the interactions between biological components. Thesemodels are:Adjacent segregation: The adjacent segregation model has been studied extensively [2]. In this model particles annihilate on contact, and...

An overview over conjugacy in semigroups
Speaker: António Malheiro (Univ. Nova de Lisboa, CMA)
When generalizing a concept, it is sometimes tempting to think that there should be one correct, or even preferred, generalization. Since semigroup theory is a vast subject, intersecting many areas of pure and applied mathematics, it is probably not reasonable to expect a one-size-fits-all...

On topological semi-abelian algebras
Speaker: Mathieu Duckerts-Antoine (CMUC)
In this talk, we will study some aspects of the categories of topological semi-abelian algebras. In particular, I will explain why these categories are homological. If the time allows it, I will also explain what is a torsion theory in a homological category and give several examples in the...

Multiplicity lists for symmetric matrices whose graphs have many edges
Speaker: Zhang Yulin (Univ. Minho)
We characterize the possible lists of multiplicities occurring among the eigenvalues of real symmetric (or Hermitian) matrices whose graph is one of Kn, Kn less an edge, or both possibilities for Kn less two edges. The lists are quite different from those for trees. Some construction...

Banach Frames and Banach Gelfand Triples, with applications to Time-Frequency Analysis
Speaker: Hans G. Feichtinger (Univ. Vienna, Austria)
It is the purpose of this talk to discuss essentially two concepts which arose in the context of time-frequency analysis (specifically relevant for Gabor Analysis), but which represent useful and fundamental functional analytic tools which certainly will be very useful also in quite...

Some results in the context of structured deformations
Speaker: José Matias (IST, Lisboa)
Structured deformations provide a model to non-classical deformations of continua suitable for the description of deformations of materials whose kinematics requires analysis at both the macroscopic and microscopic levels. We present an overview of the theory and discuss different...

BV Formality

Ricardo Campos (Univ. Zurich, Switzerland)

To a smooth manifold one can associate the Lie algebras of multivectorfields and multidifferential operators. Relating these two led Kontsevich to his famous formality theorem that establishes the deformation quantization of Poisson manifolds.In this talk we will see that if the...

Higher centrality via degenerate simplices
Speaker: Tim Van der Linden (Univ. Catholique de Louvain, Belgium)
When, in a semi-abelian category, a truncated simplicial object is considered as a higher extension, the commutators involved in the centrality condition for this extension may be expressed in terms of degenerate simplices. The aim of my talk is to explain some of the simplicial-geometrical...

The Beck-Chevalley property for Goursat categories
Speaker: Diana Rodelo (CMUC, Univ. Algarve)
We characterise regular Goursat categories through a specific stability property of regular epimorphisms with respect to pullbacks. Under the assumption of the existence of some pushouts this property can be also expressed as a restricted Beck-Chevalley condition, with respect to the...

The k-word problem over DRG
Speaker: Célia Borlido (UPorto student)
The study of finite semigroups has its roots in Theoretical Computer Science. In particular, in the mid nineteen seventies, Eilenberg [2] established the link between "varieties of rational languages", which is an important object of study in Computer Science, and certain classes...

n-Algebras admitting a multiplicative basis
Speaker: José M. Sánchez Delgado (CMUC)
See the attached file....

Singular foliations and Lie-infinity algebroids
Speaker: Camille Laurent-Gengoux (Univ. Lorraine, France)
We will describe a natural L-infinity structure associated to a singular foliation, and explain why they give the geometry of the foliation, like its monodromy. We shall relate this to several classical constructions using Lie groupoids or bisubmersions. Joint work with Sylvain Lavau and...

On convolution type operator with piecewise continuous symbols on variable Lebesgue spaces
Speaker: Oleksiy Karlovych (Univ. Nova de Lisboa)
See the attached file. ...

Non-smooth atomic decomposition of 2-microlocal spaces with variable integrability
Speaker: Helena Gonçalves (Technische Univ. Chemnitz, Germany)
The abstract is in the attached pdf file...

Besov and Triebel-Lizorkin spaces with variable exponents
Speaker: Helena Gonçalves (Technische Univ. Chemnitz, Germany)
See the attached file. Helena Gonçalves is working as a Research Assistant at Chemnitz University of Technology, Germany in the area of "Analysis" under the supervision of Prof. Henning Kempka.The seminar takes place in PORTO. ...

Geometry of numerical range of linear pencils
Speaker: Fatemeh Esmaeili Taheri (CMUC)
See the attached file....

On a version of homological algebra in the category of semimodules and its applications
Speaker: Alex Patchkoria (A. Razmadze Math. Institute of Tbilisi State Univ., Georgia)
We develop a version of homological algebra for semimodules which enables us to: (1) introduce new cohomology monoids of an arbitrary monoid M with coefficients in semimodules over M as more computable alternatives to the old ones, (2) construct singular ...

On mixed and stabilized finite element methods for the obstacle problem
Speaker: Juha Videman (IST, Univ. Lisboa)
The abstract is in the attached pdf file...

Systems of PDEs in porous media
Speaker: Léonard Monsaingeon (IST, Lisboa)
In this talk I will investigate systems of parabolic PDEs in porous media, describing competitive adsorption phenomena in groundwater contaminant models. The system is degenerate and does not fall into the general class of models studied by Alt and Luckhaus, mainly due to the non-convex...

The action of a 2-group on a category and its application in higher gauge theory
Speaker: Roger Picken (IST, Univ. Lisboa)
The fundamental notion of symmetry can be expressed as the action of a group on a set, or more generally in terms of a transformation groupoid. In this talk I will show how a group action on a set may be generalized to a 2-group action on a category C, and how such an action gives rise to a...

Howson's property for semidirect products of semilattices by groups
Speaker: Filipa Soares de Almeida (CEMAT and ISEL, Lisboa)
Howson's Theorem (1954), a classical result in group theory, established that the intersection of two finitely generated subgroups of a free group always yields a finitely generated subgroup. Jones and Trotter (1989) showed that is not the case for any free inverse semigroup with more than...

The spectral inclusion regions of linear pencils and numerical range
Speaker: Fatemeh Esmaeili Taheri (CMUC)
Let A,B be n×n (complex) matrices. We are mainly interested in the study of the structure of the spectrum of a linear pencil, that is, a pencil of the form A−λB, where λ is a complex number. Our main purpose is to obtain spectral inclusion regions for the pencil...

Toric constructions of monotone Lagrangian submanifolds in CP^2 and CP^1 x CP^1
Speaker: Agnès Gadbled (Univ. Porto)
In a previous paper, I proved that two very different constructions of monotone Lagrangian tori are Hamiltonian isotopic inside $\mathbb{CP}^2$ by comparing both of them to a third one called modified Chekanov torus. This modified Chekanov torus has an interesting projection under the...

Computational modeling of hematopoietic stem/progenitor cells expansion and differentiation
Speaker: Javad Hatami (Univ. Minho)
Quantifying the effect of exogenous parameters regulating hematopoietic stem/progenitor cells (HSC/HPC) expansion and differentiation will enhance to design robust and efficient protocols to be used for cell‐based therapies. Herein, a computational model was developed that...

The Universal Generalization Problem. Euclid's mathematical solutions and contemporary formal accounts

Pierluigi Graziani (University of Chieti-Pescara - Italy)

The goal of my talk is to analyze different contemporary foundations of Euclid's Geometry [1], compare them with each other and with the philological studies of ancient texts. In particular, I will analyze how these foundational studies fare with respect to the Universal Generalization...

The poset of proper divisibility
Speaker: Antonio Macchia (CMUC)
Inspired by the definition of the Buchberger graph of a monomial ideal, we study proper divisibility of monomials as a partial order in N^n, from a combinatorial and topological point of view. From this order relation we obtain a new family of posets, that we call posets of proper...

Exponential splitting methods for the time integration of the Klein-Gordon equation with Hagstrom-Warburton high-order absorbing boundary conditions
Speaker: Ana M. Portillo (Univ. Valladolid, Spain)
Klein-Gordon equations on an unbounded domain are considered in one dimensional and two dimensional cases. Numerical computation is reduced to a finite domain by using the Hagstrom-Warburton high-order absorbing boundary conditions. The space discretization is reached by means of finite...

An overview on the dimension of projected patterns in reaction-diffusion systems
Speaker: Juliane Fonseca de Oliveira (UPorto student)

Tuning polymeric and drug properties in a drug-eluting stent: a numerical study
Speaker: Jahed Naghipoor (ISM, Bauhaus-Universität Weimar, Germany)

Change of matrix eigenvalues multiplicity associated with perturbation of a diagonal element or deletion of a row and column
Speaker: Antonio Leal Duarte (CMUC, Univ. Coimbra)
Given an nxn matrix A, an eigenvalue λ of A and an index i (1\le i \le n) we say that i is downer (respectively neutral or Parter), if the multiplicity of λ in the matrix A(i) (obtained from A by deleting row and column i is smaller (resp equal or greater) than the...

Homotopy theory of 2-categories
Speaker: Benjamín Alarcón Heredia (CMA, FCT-UNL)
The category of small categories has a Thomason model structure making its homotopy category equivalent to the classical homotopy category of topological spaces. The same is true for small 2-categories, so we can think of small 2-categories as spaces. In this talk I will present the...

The rank of variants of nilpotent pseudovarieties

M. Hossein Shahzamanian C. (CMUP, Univ. Porto)

In this talk, we investigate the rank of classes defined by several of the variants of nilpotent semigroups in the sense of Mal'cev. For several of them, we even give finite basis of pseudoidentities. We show that the pseudovariety $\mathsf{NT}$ has infinite rank and, therefore, it is...

From medical images to computational hemodynamics: a robust pipeline
Speaker: Ana J. João (CEMAT-IST, ULisboa)
In the past decade, with the proliferation of technology and the increase of its capability, Computational Fluid Dynamics (CFD) has become a popular tool in several applications. This combined with our desire of increasing human life expectancy has lead to the combination of CFD and...

The electrostatic limit for the Zakharov system
Speaker: Luigi Forcella (Scuola Normale Superiore di Pisa, Italy)
The Zakharov system describes the coupled dynamics of the electric field amplitude and the low frequency fluctuation of the ions in a unmagnetized or weakly magnetized plasma. This system couples Schrödinger-like and wave equations and in its physical derivation depends on a parameter...

Analogies between optimal transport and minimal entropy
Speaker: Luigia Ripani (Univ. Claude Bernard Lyon 1, France)
The Schrödinger problem is an entropic minimization problem and it's a regular approximation of the Monge-Kantorovich problem, at the core of the Optimal Transport theory.In this talk I will first introduce the two problems, then I will describe some analogy between optimal transport...

Relaxation in BV×Lp
Speaker: Graça Carita (Univ. Évora)
An integral representation result is obtained for the relaxation of a class of energy functionals depending on two vector fields u in BV and v in Lp with 1<p≤+∞. This energy have been introduced to deal with equilibria for systems depending on...

The Taylor property in non-negative autoregressive stochastic processes
Speaker: Cristina Martins (DMUC, Univ. Coimbra)
In this talk we analyse the presence of the Taylor property in linear models. Limiting the study to non-negative models, we begin by recalling the main theoretical results on the occurrence of the Taylor property in autoregressive models of order one. These results are discussed in models...

What is Nelson's admissibility condition?
Speaker: Tim Van der Linden (Université Catholique de Louvain, Belgium)
In his Ph.D.thesis [3], Nelson Martins-Ferreira introduced a technical condition (for a certain type of diagram in a category) which he called admissibility. His first aim was to efficiently describe internal categorical structures, but the flexibility of the condition allowed him to use it...

A characterization of central extensions in the variety of quandles
Speaker: Andrea Montoli (CMUC, Univ. Coimbra)
The category of symmetric quandles is a Mal'tsev variety whose subvariety of abelian symmetric quandles is the category of abelian algebras. We give an algebraic description of the quandle extensions that are central for the adjunction between the variety of quandles and its subvariety of...

A numerical solution for a governing equation of Lévy motion
Speaker: Ercília Sousa (CMUC, Univ. Coimbra)
This study looks at a governing equation of Lévy motion. This governing equation is a generalization of the classical, deterministic advection diffusion equation, just as Lévy motion is a generalization of Brownian motion. It can be represented by fractional derivatives, which...

A tropical approach to stable spin curves
Speaker: Ana Margarida Melo (CMUC, Univ. Coimbra)
The moduli space of spin curves of genus $g$ parametrizes pairs consisting of a curve and a square root of the canonical class on the curve. It is therefore endowed with a forgetful map to $M_g$, the moduli space of curves of genus $g$, which has degree $2^{2g}$. There are different modular...

Groupoids, fibrations and rigidity
Speaker: Matias del Hoyo (IMPA, Brazil)
Fibred categories were introduced in descent theory by A. Grothendieck. In this talk I will discuss fibred Lie groupoids, an incarnation of that formalism in differential geometry, studied by K. Mackenzie, among others. In a joint work with R. Fernandes we construct suitable metrics on...

On pseudovarieties of forest algebras
Speaker: Saeid Alirezazadeh
Forest algebras are used in the theory of formal languages. They consist of two monoids, the horizontal one H and the vertical one V , with an action of V on H, and a complementary axiom of faithfulness. The main example is the forest algebras of plane forests and contexts, that is to say...

A distance on the space of Radon measures with application to spatial population dynamics
Speaker: Stanislav Kondratyev (CMUC, Univ. Coimbra)
We introduce a new optimal transport distance between nonnegative finite Radon measures, derive associated Riemannian structure and develop an Otto calculus.  As an application, we identify a model in spatial population dynamics as a gradient flow and obtain long-time convergence...

Rolling maps and applications
Speaker: Fátima Pina
Rolling motions are rigid motions subject to holonomic and nonholonomic constraints. These motions appear associated to certain engineering areas, such as robotics and computer vision. Rolling maps are the mathematical tools to describe rolling motions.In this talk, the concept of rolling...

Invariant factors of matrices over general rings
Speaker: Joao Filipe Queiró (CMUC, Univ. Coimbra)
This talk is a report on recent work with Cristina Caldeira concerning invariant factors of products of matrices over the class of elementary divisor domains. For an nxn matrix over such a ring R, and a pure submodule of R^n, we define a new type of "Rayleigh functional" and use...

Biadjoint triangles, descent and coherence
Speaker: Fernando Lucatelli Nunes (CMUC, Univ. Coimbra)
Firstly, we talk about the general result of coherence due to Power-Kelly-Blackwell and Lack. Then, we show how this motivates the study of a 2-dimensional version of Eduardo Dubuc's adjoint triangle theorem.At last, we show what the proofs of the (bi)adjoint triangle theorems have to do...

Functional representations of monads in duality theory
Speaker: Pedro Nora (Univ. Aveiro)
It is well known that Stone's classical duality theorems can be generalised to categories of spaces and continuous relations. For example, Halmos's duality theorem affirms that the category of Stone spaces and Boolean relations (relations which are continuous in an appropriate sense) is...

A coupled release-absorption model for drug delivery systems
Giuseppe Pontrelli (Istitupo per le Applicazioni del Calcolo, Rome, Italy)
In this talk I will present a mathematical model describing the release from a drug delivery system, such as a coronary eluting stent or a transdermal patch.The problem is reduced to a dynamics of a two-phase substance between two coupled  media of different properties and extents. The...

Approximation numbers of weighted Sobolev embeddings via bracketing
Speaker: Therese Mieth (Friedrich-Schiller-Univ. Jena, Germany)

Heegaard genus and rank of link complements
Speaker: Darlan Girão (Univ. Federal Ceará, Brazil)
In this talk we will discuss the relationship between the Heegaard genus and rank of 3-dimentional manifolds. Despite some recent advances in this topic, little is known for manifolds arising as link complements in S^3. We will provide a very rich class of link complements for which rank...

Birationality of moduli spaces of twisted U(p,q)-Higgs bundles
Speaker: Azizeh Nozad (Univ. Porto)
Let X be a Riemann surface of genus g greater or equal than 2. A twisted U(p,q)-Higgs bundle consists of a pair of holomorphic vector bundles on a Riemann surface, together with a pair of twisted maps between them. Here we study the variation with the parameter of the moduli space of...

Numerical solution of time-dependent Maxwell's equations in anisotropic materials for modelling light scattering in human eye's structure
Speaker: Maryam Khaksar Ghalati
Modelling light propagation in biological tissue has become an important research topic in biomedical optics with application in diverse fields as for example in ophthalmology. Waveguides with induced anisotropy may worth to be modeled as they could play a role in biological waveguides. For...

The meet formula for pseudocomplement and an aspect of the coframe of sublocales
Speaker: Aleš Pultr (Charles Univ., Prague, Czech Republic)
 A frame is a complete Heyting algebra; in particular it is pseudocomplemented and we have the formula a^* = \bigvee{x : x \wedge a = 0}. Dually, in a coframe we have the formula for the supplement a^# = \bigwedge{x : x v a = 1}. (#) Somewhat surprisingly, under suitable (and very...

Nearly Sasakian manifolds and related structures.
Speaker: Giulia Dileo (Univ. Bari, Italy)
Nearly Sasakian manifolds are a special class of almost contact metric manifolds, providing a natural odd dimensionalcounterpart of nearly Kähler manifolds.In the present talk I will describe the main properties of nearly Sasakian manifolds, referring also to geometric structures which...

On the discriminated nondimensionalization of coupled, non-linear ordinary differential equations and system of equations
Speaker: Manuel Conesa (Univ. Politécnica de Cartagena, Spain)
The first step to simplify the analysis of a mathematical model is to search the dimensionless groups that control its solution pattern since the solution of any equation or system of equations that define the laws that rule a physical or engineering problem can be represented as a relation...

A branching process approach to the survival of populations: skeleton process and stochastic introgression
Speaker: Maria Conceição Serra (CMAT, Univ. Minho)
In this talk we present branching processes as a tool to model the evolution of populations which are, in principle, doomed to extinction but manage to survive. Survival is usually achieved through the appearance of different types of individuals that give an “advantage” to the...

Height functions on symmetric spaces
Speaker: María José Pereira-Sáez (Univ. Coruña, Spain)
Morse theory gives us useful techniques to analyze the homotopic structure of a smooth manifold studying some smooth functions on this manifold. This allows us to find the cellular structure of a CW-complex and get some information about its cohomology. We will consider here height...

Object detection, multispectral fusion, motion analysis and tracking in aerial imagery and video
Speaker: Kannappan Palaniappan (Univ. Missouri, Columbia, USA)
Visual feature-based tracking systems need to adapt to variations in the appearance of an object and in the scene for robust performance to avoid drift. Tracking in aerial imagery is challenging as viewing geometry, calibration inaccuracies, complex flight paths and back- ground changes...

Filtering, fusion, detection and segmentation of microvasculature vessel fluorescence imagery
Speaker: Kannappan Palaniappan (Univ. Missouri, Columbia, USA)
Automatic segmentation of three-dimensional microvascular structures is needed for quantifying morphological changes and remodeling of blood vessels during development, disease and treatment processes. We use an approach for vessel segmentation that combines multiple single focus images use...

Supernilpotent algebras are non-dualizable
Speaker: Wolfram Bentz (CEMAT-­FCUL, Univ. de Lisboa)
Natural dualities, such as Stone duality, are useful because they allow one to translate algebraic questions into the potentially simpler and usually more intuitive setting of a topological structure. If these dualities exist for particular classes of algebras, then they can be obtained in a...

The Karoubi envelope and the Schützenberger category of a semigroup.
Speaker: Alfredo Costa (CMUC, Univ. Coimbra)
The Karoubi envelope plays a fundamental role in Tilson's Delay theorem, an important result in the theory of pseudovarieties of semigroups. It is also known that two semigroups with local units are Morita equivalent if and only if they have equivalent Karoubi envelops.We introduce a new...

On displaceability of pre-Lagrangians in toric contact manifolds
Speaker: Milena Pabiniak (IST Lisboa)
In symplectic geometry one can observe a rigidity of intersections: certain (Lagrangian) submanifolds are forced to intersect each other in more points than an argument from algebraic or differential topology would predict. For example, every compact symplectic toric manifold contains a...

On computing efficient pairs of disjoint paths
Speaker: Marta Pascoal (INESC / Univ. Coimbra)
Pairs of disjoint paths between two nodes in a network provide a primary path as well as a backup path, such that the latter can be used in case one of the arcs of the first is not available. The problem of finding the shortest pair of disjoint paths can be formulated as a minimum cost flow...

Coistropic reduction for Poisson Lie actions
Speaker: Chiara Esposito (Univ. Wuerzburg, Germany)
In this talk we present a reduction procedure in the setting of a Poisson Lie group (G,\pi_G) acting on a Poisson manifold (M, \pi). In such cases we can introduce the notion of comomentum map and we show that, under certain conditions, it produces a Hamiltonian action on the...

Convergence of Kiefer-Wolfowitz algorithm under quasi-associated random errors
Speaker: Idir Arab (University of Bejaia, Algeria)
In this talk, we study the algorithm of Kiefer-Wolfowitz under quasi-associated random errors. We establish the complete convergence and obtain an exponential bound. Additionally, we build a confidence interval for the minimum. Numerical examples are sketched out to confirm the theoretical...

Arbitrary triple systems admitting a multiplicative basis
Speaker: José María Sánchez Delgado (Univ. Cadiz, Spain)
Let T be a triple system of arbitrary dimension, over an arbitrary base field K and in which any identity on the triple product is not supposed. A basis of T is called multiplicative if for any three elements we have that its product is a multiple (coefficient in K) of some element of the...

Modeling Dengue disease: two real outbreaks - theoretical and practical issues
Speaker: Maria Teresa Monteiro (ALGORITMI, Univ. Minho)
Epidemiology has become an important issue for modern society. Demographic evolution, accelerated urbanization, increased traveling and climate change, all favor the propagation of infectious diseases.Dengue is the most rapidly spreading mosquito-borne viral disease in the world. According...

Regularity properties of maximal functions
Speaker: Emanuel Carneiro (IMPA, Rio de Janeiro, Brazil)
In this talk I will briefly survey the regularity theory for maximal operators in Sobolev and BV spaces. It has been conjectured for more than a decade that the classical centered one-dimensional Hardy-Littlewood maximal operator should not increase the variation of a function. The...

L-infty graded manifolds, Kapranov manifolds and applications
Speaker: Camille Laurent-Gengoux (Univ. Lorraine, France)
Several linearization problems can be expressed as the linearization of a L-infty algebra for a particular type, that we call Kapranov manifold.A algebroid cohomology class, called the Atiyah class, plays there a crucial role. Joint works with Mathieu Stiénon, Yannick Voglaire and...

Quaternion Newton-like methods
Speaker: Maria Irene Falcão (Univ. Minho)
It is a well known fact that the algebraic as well as the geometric properties of complex holomorphic functions are not the same for their generalizations in quaternion analysis. In particular, because of the non-commutativity of quaternion multiplication, the use of root-finding methods...

On Auslander-Reiten sequences for simple modules in the Borel-Schur algebras
Speaker: Ana Paula Santana (CMUC/Univ. Coimbra)
I will construct Auslander-Reiten sequences for a large class of simple modules over Borel-Schur algebras. Partial information on the structure of the socles of Borel-Schur algebras will also be given.This is joint work with Karin Erdmann and Ivan Yudin....

Eigenvalues, multiplicities and graphs: recent advances and open problems
Speaker: Charles R. Johnson (College of William and Mary, Williamsburg, USA)
Let G be an undirected graph on n vertices and let S(G) denote the set of all symmetric matrices with graph G and let L(G) denote the set of all multiplicity lists occurring among the matrices in S(G). The diagonal entries of matrices in S(G) are free. There has long been study of this...

Invariant manifolds of non-autonomous ODEs
Speaker: António Bento (Univ. Beira Interior)

Primitive multiple curves: classification, moduli spaces of sheaves, deformations
Speaker: Jean-Marc Drézet (Institut de mathématiques de Jussieu, France)
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Yred is smooth. These curves have been defined and studied by C. Banica and O. Forster in 1984.In 1995, D. Bayer and D. Eisenbud gave a complete...

Kan-injectivity of locales and spaces
Speaker: Lurdes Sousa (IP Viseu and CMUC)
Two well-known important facts are the characterization of the continuous lattices as the spaces injective with respect to embeddings in the category Top0 of T0 topological spaces (D. Scott, 1972), and the characterization of the stably locally compact locales as the locales injective with...

What is an ideal a zero-class of?
Speaker: Andrea Montoli (CMUC)
We characterize, in pointed regular categories, the ideals as the zero-classes of surjective relations. Moreover, we study a variation of the ''Smith is Huq'' condition: two surjective left split relations commute as soon as their zero-classes commute.Joint work with Nelson Martins-Ferreira,...

Boundedness of Stein's spherical maximal function in variable Lebesgue space and application to the wave equation

Amiran Gogatishvili (Czech Academy of Sciences, Czech Republic)

The abstract is in the attached pdf file...

Wavelets in Economics and Political Science
Speaker: Maria Joana Soares (Univ. Minho)
The use of wavelet analysis is already very common in a large variety of disciplines, such as physics, geophysics, signal and image processing, medicine, biology, etc. More recently, wavelet tools have also been applied successfully in the areas of economics and finance. In spite of their...

Harmonic Analysis for the Natural Sciences II
Speaker: Luís Daniel Abreu (ARI-Austrian Academy of Sciences)
This is a continuation of Wednesday's talk on the Numerical Analysis seminar. After a short presentation of the program, I will focus on the new approach to the localization problem which is being developed with João M. Pereira, a former student of DMUC....

Harmonic Analysis for the Natural Sciences
Speaker: Luís Daniel Abreu (ARI-Austrian Academy of Sciences)
In the Natural Sciences, researchers are often faced with three problems of significant mathematical complexity. The first problem arises in every science where the observation process plays an important role: the need of restricting their measurements to a subregion of the ambient...

Kinetic theory of simple reacting spheres: modelling and hydrodynamic regimes
Speaker: Ana Jacinta Soares (Univ. Minho)
In the frame of the kinetic theory of chemically reacting gases, we consider the model of simple reacting spheres (SRS) in a moderately dense gas regime. The gas molecules behave as if they were single mass points and collisions result in chemically reactive encounters when the kinetic...

Computational hydrodynamics, from theory to practice
Speaker: José S. Antunes do Carmo (Marine and Environmental Sciences Centre/UC)
In the 80’s, numerical models based on the Saint-Venant equations, or shallow water equations, were frequently used in practical applications. However, as has been widely demonstrated, in shallow water conditions and for some types of waves, models based on a non-dispersive theory, of...

Monóides de Ehresmann
Speaker: Gracinda M.S. Gomes (DM-­FCUL e CEMAT-­FCUL, Univ. Lisboa)
Na teoria dos monóides inversos a classe dos próprios, ou E-­unitários, tem um papel crucial, já que todo o monóide inverso tem uma cobertura própria (que separa idempotentes), um monóide inverso próprio ...

Borel-Schur algebras of finite representation type
Speaker: Ivan Yudin (CMUC)
In my talk I will explain what is the representation type of a finite dimensional algebra. Then I will describe the Borel-Schur algebras of finite type. This is a joint work with K. Erdmann and A.P. Santana....

A Néron model of the universal jacobian
Speaker: David Holmes (Univ. Leiden, The Netherlands)
Every non-singular algebraic curve C has a jacobian J, which is an abelian variety. Choosing a point on the curve determines an `abel-jacobi' map from C to J. The same constructions can be made in families: given a family of non-singular curves (together with a section), one obtains a family...

An optimal design problem with fractional diffusion
Speaker: Rafayel Teymurazyan (CMUC)
We study an optimization problem ruled by a-fractional diffusion operator with volume constraint. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of class C0,\alpha, and that the free boundary is a C1,\alpha surface, up to a...

Assessment of image derived PET quantification techniques
Speaker: Miguel Patrício (Lab. Biostatistics and Medical Informatics, IBILI-FMUC)
Data detected by a positron emission tomography (PET) scanner is translated into concentration of radiotracer by using image reconstruction methods. Applying reconstruction algorithms will only retrieve the radiotracer concentration. However, there will be no discrimination between...

The exact discrete Lagrangian function in the Lie groupoid setting
Speaker: Juan Carlos Marrero (Univ. de La Laguna, Spain)
In this talk, I will present a definition of the exact discrete Lagrangian function associated with a continuous regular Lagrangian function on the Lie algebroid of a Lie groupoid. A result on variational analysis error in this setting will also be presented. In order to define the exact...

Rolling pseudo-Riemannian submanifolds
Speaker: André Marques (Instituto Politécnico de Viseu)
We present an overview about rolling motions, subject to non-slip and non-twist constraints, of manifolds which are embedded in pseudo-Riemannian manifolds. Within this general framework, we analyze the individual cases of rolling of pseudo-hyperbolic spaces and quadratic Lie groups. We...

Covers of the projective plane
Speaker: Eduardo Dias (Univ. Warwick, UK)
The problem of describing the equations of a projective model of an irregular variety is often a difficult one. In this talk we will focus on the case of irregular surfaces. We will describe the construction of the projective model of an Abelian surface with a polarization of type (1,3) via...

Peiffer product and Peiffer commutator for internal pre-crossed modules
Speaker: Alan S. Cigoli (Università degli Studi di Milano, Italy)
In this work we introduce the notions of Peiffer product and Peiffer commutator of internal pre-crossed modules over a fixed object B, extending the corresponding classical notions to any semi-abelian category. We prove that, under mild additional assumptions on the category, crossed modules...

The localic group of the unit circle

Imanol Mozo Carollo (UPV/EHU, Bilbao, Spain) 

The category of locales, which is the object of study of pointfree topology, has an algebraic dual, the category of frames. This fact was used by Joyal in order to introduce the frame of reals as a pointfree counterpart of the real line [3]. Further, this lead to a fruitful study of the...

Modeling blood flow and mass transport by a drug eluting stent
Speaker: Elias Gudiño (IST, Lisboa)
In this seminar we will present a fully coupled model for the description of blood flow and mass transport by a drug eluting stent in blood vessels. In order to obtain a numerical solution of the problem, we use an iterative splitting scheme over a stabilized finite element method together...

About embeddings and minimal action solutions of elliptic equations
Speaker: Eugénio Rocha (Univ. Aveiro)
in the attached file ...

Invariant theory and descent via symmetric monoidal categories
Speaker: Ehud Meir (Univ. Copenhagen, Denmark)
Let C be a symmetric monoidal K-linear category, where K is an algebraically closed field of characteristic zero.  Deligne proved that if C satisfies a certain finiteness assumption, then C is necessarily equivalent to the category Rep_K-G, of the finite dimensional rational...

Modelling with clinical data: examples, limitations, aims ...
Speaker: Carla Henriques (CMUC and Instituto Politécnico de Viseu)
In this seminar, we will present some examples of applications of Statistics in the field of Medicine. Research questions are posed by health professionals, who aim to see their "sensibilities" supported statistically. The answers are not always straightforward, and the...

Orthogonal polynomial interpretation of \Delta-Toda and Volterra lattices
Speaker: Ana Foulquié Moreno (Univ. Aveiro)
The correspondence between dynamics of $\Delta$-Toda and $\Delta$-Volterra lattices for the coefficients of the Jacobi operator and its resolvent function is established. A method to solve inverse problem --integration of $\Delta$--Toda and $\Delta$-Volterra lattices -- based on Pad\'e...

Plactic, hypoplactic, and Sylvester monoids, and other homogeneous monoids
Speaker: Alan Cain (CMA, Univ. Nova de Lisboa)
In recent work with Gray and Malheiro, I proved that finite-rank plactic monoids (in which Young tableaux form a cross-section) admit finite convergent presentations and are biautomatic. This seminar will survey three themes arising from this work: (1) Using similar techniques with rather...

Sasakian nilmanifolds
Speaker: Antonio De Nicola (CMUC, Univ. Coimbra)
Sullivan's theory of models can be used to get topological invariants of manifolds that are stronger than the de Rham cohomology ring.One defines a model for a manifold as a commutative differential graded algebra (CDGA) quasi-isomorphic to the algebra of differential forms. It is known that...

Some recent mathematical ideas for applications in biology
Speaker: Ezio Venturino (Univ. Torino, Italy)
In this talk classical models in ecology and epidemiology will be presented and reviewed. These two fields have grown independently for a long time. Scientists have treated them separately, but only fairly recently have begun to realize that they do influence one another profoundly. Some...

A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations
Speaker: Léonard Monsaingeon (IST, Univ. Lisboa)
The abstract is in the attached pdf file...

On Randic spread
Speaker: Enide Andrade (Univ. Aveiro)
A new spectral graph invariant spr(R), called Randic spread, is defined and investigated. This quantity is equal to the maximal difference between two eigenvalues of the Randic matrix, disregarding the spectral radius. Lower bounds for spr(R) are deduced, some of which depending on the Randi...

Modeling and analysis of count data time series: recent research activities
Speaker: Christian H. Weiß (Helmut Schmidt Univ. Hamburg, Germany)
After a brief introduction to basic concepts and examples of count data time series, we shall focus on two particular models and their statistical analysis: the (compound) Poisson INAR(1) model and the (self-exciting threshold) binomial AR(1) model.The Poisson INAR(1) model is the most...

Hexagonal projected symmetries
Speaker: Juliane Oliveira (Univ. Porto)
Three-dimensional symmetries are often observed as 2-dimensional objects. In this seminar we will provide a description of which 3-dimensional lattices may produce 2-dimensional projected pattern with hexagonal symmetries. As an application we compare some projected spatially periodic...

Compactness in quasi-Banach function spaces
Speaker: António Caetano (Univ. Aveiro)
The well-known criterion for the precompactness of sets in a Banach function space states that a subset K of the absolutely continuous part Xa of a Banach function space X is precompact in X if and only if K is locally precompact in measure and K has uniformly absolutely...

From ordered to metric compact Hausdorff spaces
Speaker: Dirk Hofmann (Univ. Aveiro)
The aim of this talk is to lift the well-known equivalence between ordered compact Hausdorff spaces and stably compact spaces to the metric world, together with several constructions involving these types of spaces....

On the "Smith is Huq" condition in S-protomodular categories
Speaker: Andrea Montoli (CMUC)
We study the so-called "Smith is Huq" condition in the context of S-protomodular categories: two S-equivalence relations centralise each other if and only if their normalisations commute. We prove that this condition is satisfied by every category of monoids with operations...

Numerical modeling of complex fluid flows using the Finite Volume Method
Speaker: Luís Ferrás (Inst. Polímeros e Compósitos, Univ. do Minho)
In this work we present a study on flows of Newtonian and Non-Newtonian fluids, carried out both analytically and numerically. Industrial applications of these flows are found in classical industries such as in polymer processing (for instance in extrusion) and in more modern applications as...

Density-based cluster analysis: an interface between Statistics, Differential Topology and Dynamical Systems
Speaker: José E. Chacón (Univ. de Extremadura, Spain)
Despite its popularity, the investigation of some theoretical aspects of clustering has been relatively sparse. One of the main reasons for this lack of theoretical results is surely the fact that, unlike the situation with other statistical problems as regression or classification, for some...

Monoid theoretic approach to bicategorical structures
Speaker: Dimitri Chikhladze (CMUC, Univ. Coimbra)
We develop a lax version of the formal theory of monads, and consider its connection with the bicategorical structures and the theory of generalized operads. ...

Kaehler-Lie systems and geometric quantum mechanics
Speaker: Jesús Clemente-Gallardo (Univ. Zaragoza, Spain)
In this seminar we will study an application of the geometric formulation of Quantum Mechanics to study Lie systems on finite-dimensional complex manifolds. We will present the geometric methods developed to study their superposition rules, time independent constants of motion, Lie...

Orthogonal polynomials and random matrices
Speaker: Alfredo Deaño (Univ. Carlos III, Madrid, Spain)
In this talk we present some classical results on unitarily invariant ensembles of random matrices of size NxN, the prime example being the Gaussian Unitary Ensemble (GUE). It will be shown how the analysis of the corresponding family of orthogonal polynomials on the real line can be used...

Quasi-F frames
Speaker: Mack Matlabyana (Univ. Limpopo, South Africa)
A completely regular frame L is said to be quasi-F if for every dense c ∈ CozL, the open quotient L →↓a is a C*-quotient map.Quasi-F frames generalize almost-P frames and F'-frames. The intention of the talk is to give several characterizations of these frames....

On topological semi-abelian algebras: split extensions and their classifiers
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
Actions of a group B on a group X correspond bijectively to split extensions of B with kernel X, or to semidirect products of X and B, or to group homomorphisms from B to the group Aut(X) of automorphisms of X. This last property of Aut(X) is usually identified as representability of...

Bi-periodic solutions to the Fokker-Planck equation and operation of Brownian motors
Speaker: Dmitry Vorotnikov (CMUC, Univ. Coimbra)
We study the unidirectional transport effect for Brownian ratchets modeled by Fokker--Planck-type equations. In particular, we consider the adiabatic andsemiadiabatic limits for tilting ratchets, generic ratchets with small diffusion, and the multi-state chemical ratchets. Having...

Hypermaps and their classifications
Speaker: Domenico Antonino Catalano (Univ. Aveiro)
Problems in hypermap theory have applications to many branches of mathematics. This is a consequence of the different interpretations of the notion of a hypermap. A hypermap is-A representation of a hypergraph (Combinatorics);-A triangulation of a compact surface (Topology);-A quotient of an...

Split Lie algebras and relations with weight modules
Speaker: José M. Sánchez Delgado (Univ. Cádiz, Spain)
We begin by reviewing the main results of the theory of finite dimensional Lie algebras. We continue by considering the class of split Lie algebras of arbitrary dimension. As a generalization, we study the structure of weight modules over< split Lie algebras.We show that under certain...

Random fields and random sampling
Speaker: Maria da Graça Temido (CMUC, Univ. Coimbra)
This talk is focused on the study of the maximum term of a stationary bivariate random field. Considering the double random dimensions with asymptotic geometric growing pattern, in probability, a mixture distribution for the maximum is established. ...

Connected components of character varieties and Higgs bundles
Speaker: André G. Oliveira (UTAD)
Given a compact Riemann surface X and a real reductive Lie group G, let  R_G=Hom^{red}(\pi_1 X,G)/G be the space of reductive representations of \pi_1 X in G, the so-called G-character variety of X. This is a space with a very rich topological structure, reflecting the topology of both...

Constrained optimization techniques for quadratic matrix model updating

Marcos Raydan (Univ. Simón Bolívar, Venezuela)

The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric second-order finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from...

Noncrossing partitions in negative CY triangulated categories
Speaker: Raquel Coelho Guardado Simões (Univ. Lisboa)
A key way to understand triangulated categories is to look at generators. In the context of positive Calabi-Yau (CY) triangulated categories, such as cluster categories, the most interesting generators seem to be cluster-tilting objects. There are some triangulated categories which are...

Extreme Value Theory for chaotic dynamics
Speaker: Jorge Milhazes Freitas (CMUP, Univ. Porto)
We will give an introduction to the Extreme Value Theory in a dynamical systems context. In particular, we will interpret the occurrence of rare events in terms of the hitting time to certain shrinking targets on the phase space of the possible states of a given system. We will present new...

Involutive double categories
Speaker: Rachel A.D. Martins (IST/UL)
A double category has an equivalent description as a double partial monoid, that is, a set equipped with two partial monoid structures such that all structure maps are partial monoid homomorphisms. Double categories can have an interesting and natural involutive structure, which we ...

Some remarks on descent for Priestley spaces
Speaker: Manuela Sobral (CMUC, Univ. Coimbra)
In this talk the problem of characterizing effective descent morphisms for Priestley spaces is recalled and solved in two veryspecial cases: for maps with finite codomain and for maps that are open and order-open, or, equivalently, open and order-closed....

Uniform convergence of Hermite-Padé approximants for systems of Markov type functions
Speaker: Sergio Medina Peralta (Univ. Carlos III, Madrid, Spain)
This talk deals with simultaneous rational approximation. In particular we study Hermite-Padé approximants of analytic and meromorphic functions of Markov type. The central results of this work is about of convergence of type I Hermite-Padé approximants of a Nikishin system....

The MOOD method, principle and (some) examples
Speaker: Stéphane Clain (Univ. Minho)
We present a new finite volume method to provide 6th-order approximations for hyperbolic problems.The technique is based on the one hand to a conservative polynomial reconstruction which enableto  provide local accurate representations and an a posteriori limitation to prevent from...

Limiting embeddings in smoothness Morrey spaces, and applications
Speaker: Dorothee D. Haroske (Univ. Jena, Germany)

Computational methods in the fractional calculus of variations
Speaker: Delfim F. M. Torres (Univ. Aveiro)
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, allowing problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional...

Combinatorial Brill-Noether theory
Speaker: Jorge Sentieiro Neves (CMUC / Univ. Coimbra)
The theory of linear systems on graphs is a recent branch of combinatorics owing its fast development to a link with algebraic and tropical geometry. We will review the general theory leading up to the Brill-Noether theorem, whose purely combinatorial proof is an open problem....

Fundamental group functors and higher Hopf formulae
Speaker: Mathieu Duckerts-Antoine (CMUC)
In 1988, R. Brown and G. J. Ellis gave Hopf formulae for the integral homology of a group using topological methods. G. Janelidze first recognized that these descriptions are deeply connected with the categorical Galois-theoretic notion of covering morphism. Using this perspective, T....

Lax algebras as spaces
Speaker: Maria Manuel Clementino (CMUC, Univ. Coimbra)
Following [1], in this talk we look at lax algebras as spaces, exploring their topological properties like compactness, Hausdorff separation, regularity, normality and extremal disconnectedness. [1] M.M. Clementino, E. Colebunders, W. Tholen, Lax algebras as spaces, in: Monoidal...

On approximation by periodic splines: theory and application
Speaker: Rolf D. Grigorieff (Technische Univ. Berlin, Germany)
The talk is concerned with the existence of multiple knot periodic splines satisfying general Hermite interpolation conditions and their approximation power in Sobolev spaces. The key for such results are necessary and sufficient conditions for the existence of interpolating cardinal splines...

A new class of integer valued processes with conditional heteroscedasticity
Speaker: Filipa Silva (CMUC)
The aim of this talk is to introduce an integer-valued model with conditional distribution belonging to the class of compound Poisson probability laws. This proposal includes, in particular, the Poisson INGARCH model, and the negative binomial and generalized Poisson models. We show the...

Electrostatic interpretation of roots of polynomials satisfying certain 2nd order differential equations
Speaker: Edmundo Huertas Cejudo (CMUC)
In the last years some attention has been paid to the so called canonical spectral transformations of measures. This talk is focused on the behaviour of zeros of monic orthogonal polynomial sequences (MOPS in short) associated with the so called Geronimus canonical transformation, which...

The pointfree representation of a truncated archimedean l-group
Speaker: Richard N. Ball (Univ. Denver, USA)
In this talk we develop the analog for truncated archimedean lattice-ordered groups, hereafter referred to as truncs, of Madden's pointfree representation for W, the category of archimedean l- groups with designated weak order unit. In the first part of the talk we will motivate the notion...

Pointfree pointwise suprema in archimedean l-groups
Speaker: Richard N. Ball (Univ. Denver, USA)
We generalize the concept of the pointwise supremum of real-valued functions to the pointfree setting. The concept itself admits a direct and intuitive formulation which makes no mention of points. But our aim here is to investigate pointwise suprema of subsets of RL, the family of...

Mathematics in Industry: Some successful collaborations
Speaker: Manuel B. Cruz (LEMA/ISEP)
The interaction Mathematics-Industry has suffered a great development in the latest years. The genesis of EU-MATHS-IN, the European Network for Mathematics in Industry, as well as the spread of several national networks across Europe, illustrates the evolution and potential of that area of...

An overview of some Spanish infrastructure focused on promoting the transfer of mathematics to industry
Peregrina Quintela (Univ. Santiago de Compostela)
In the talk two infrastructures aimed at boosting transfer to industry will be presented: The Spanish Network for Mathematical and Industry (math-in) and the Technological Institute of Industrial Mathematics (ITMATI). Some details of how they were formed, the type of legal entity chosen, the...

Optimal basis algorithm and its application to matrix scaling
Speaker: Oleg Burdakov (Linköping Univ., Sweden)
We present the optimal basis (OB) problem and the OB algorithm that we proposed in BIT (1997) {\bf 37}, 591-599. The OB problem is formulated as follows. Given $m+1$ points $\{x_i\}^{m}_{0}$ in $R^n$ which generate an $m$-dimensional linear manifold, construct for this manifold a maximally...

Dimension counts for singular rational curves
Speaker: Ethan Cotterill (Univ. Federal Fluminense, Niterói, Brazil)
Rational curves are essential tools for classifying algebraic varieties. Establishing dimension bounds for families of embedded rational curves that admit singularities of a particular type arises naturally as part of this classification. Singularities, in turn, are classified by their value...

Composition factors of a tensor product of several symmetric powers
Speaker: Stephen Donkin (Univ. of York, UK)
We consider the problem of determining which irreducible polynomial modules occur as a composition factor of an m-fold tensor product of symmetric powers of the natural module for the general linear group. The case m=1 was analysed by Krop and Sullivan and they obtained (independently) a...

Mehler-Heine asymptotics of polynomials
Speaker: Juan J. Moreno Balcázar (Univ. Almeria, Spain)
In this talk, we will give an overview about Mehler--Heine asymptotics of polynomials. This type of formulae is well known for very classical Jacobi, Laguerre and Hermite polynomials. We pay attention to recent results obtained for other families of polynomials such as generalized...

The spectral theorem on the para-orthogonality theory
Speaker: Kenier Castillo (UNESP, Brazil)
Our goal is to provide the para-orthogonality theory with a new powerful tool for computing: recurrence relation. Analogous results to the classicals Favard and Geronimus-Wendroff theorems are deduced....

Compact embeddings of weighted Sobolev spaces
Speaker: Therese Mieth (Friedrich-Schiller-Univ. Jena, Germany)
The abstract is in the attached pdf file ...

Kan-injectivity in Top0 and Kan-projectivity in Frm
Speaker: Margarida Carvalho (ISCAC)
In the context of categories enriched in the category of partial order sets, we will work with KZ-reflectivity and Kan-injectivity, notions which, as we shall see, are closely related.We will show that there is an infinite chain of small subcategories of the category Top0, whose...

Lax orthogonal factorisation systems
Speaker: Maria Manuel Clementino (CMUC)
In [4] Grandis and Tholen introduced natural weak factorisation systems (also called algebraic weak factorisation systems, see [3]) as pairs (L,R), where L is a comonad and R is a monad subject to suitable conditions, and showed that orthogonal factorisation systems are the natural weak...

Generalizations of generating functions for orthogonal polynomials in the Askey and q-Askey schemes
Speaker: Howard S. Cohl (National Institute of Standards and Technology, USA)
In this talk, we present generalized generating functions for generalized hypergeometric and basic hypergeometric orthogonal polynomials. These generalized expansions are obtained by re-expressing the polynomials in the generating functions using multi-parameter connection relations. The...

Non-Fickian models for biodegradable drug eluting stents
Speaker: Jahed Naghipoor (CMUC)
In recent years, mathematical modeling of cardiovascular drug delivery systems has become an effective tool to gain deeper insights in the cardiovascular diseases like atherosclerosis. In the case of coronary biodegradable stent which is a tiny expandable metallic mesh tube covered by...

Effective cones of higher codimension cycles on moduli spaces of curves
Speaker: Izzet Coskun (Univ. of Illinois at Chicago, USA)
I will report on joint work with Dawei Chen where we study effective cones of higher codimension cycles on moduli spaces of curves.We show certain geometrically defined cycles span extremal rays in the effective cone. In particular, we prove that codimension two boundary strata are extremal....

On Butler's conjecture
Speaker: Leticia Brambila-Paz (CIMAT, Mexico)
D.C. Butler conjectured that the kernel of the evaluation map of a general generatedcoherent system over a general curve is stable. In this talk I will explain theproof of the conjecture for linear series. This is a joint work with Usha Bhosleand Peter Newstead....

Hypersymplectic and hyperkähler structures with torsion
Speaker: Paulo Antunes (CMUC)
We define hypersymplectic structures with torsion (HST) on Lie algebroids and establish a 1-1 correspondence between hyperkähler structures with torsion (HKT) and HST structures. We also obtain a contravariant definition of both HKT and HST structures on Lie algebroids. Additionally, we...

Towards a calculus of fractions concerning Kan-injectivity
Speaker: Lurdes Sousa (CMUC and IP Viseu)
In an order-enriched category $\cal X$, for a given subcategory $\cal A$, we study the class ${\cal A}^{KInj}$ of all morphisms with respect to which $\cal A$ is Kan-injective. We show that, for $\cal A$ an arbitrary subcategory of $\cal X$, ${\cal A}^{KInj}$ is, in a certain sense, closed...

The Karoubi envelope of sofic, Markov-Dyck and Property (A) shifts
Speaker: Alfredo Costa (CMUC)
In this talk, we discuss some recent results, obtained jointly with Benjamin Steinberg, about the Karoubi envelope of the syntactic semigroup of a shift. We see that, in a natural way, the Karoubi envelope is the best possible syntactic invariant of flow equivalence of sofic shifts. ...

The average covering number of a graph
Speaker: Derya Dogan (Celal Bayar Univ., Turkey)
There are occasions when an average value of a graph parameter gives more useful information than the basic global value. In this talk, we introduce the concept of the average covering number of a graph (the covering number of a graph is the minimum number of vertices in a set with the...

Boundary integral methods using implicitly defined interfaces and their applications
Speaker: Richard Tsai (Univ. of Texas at Austin, USA)
I will describe a new framework for building numerical methods for boundary integral equations using implicit surface representation. Such setting is natural for many problems that involve bulk-diffusion driven nonlinear interface dynamics in irregular and unbounded domains. Typically the...

Polar maps, foliations, characteristic classes
Speaker: Nivaldo Medeiros (Univ. Fluminense, Brazil)
To each hypersurface X in the projective n-space, we associate a rational map Pn--->Pn, called its polar map, given simply by the partial derivatives of the polynomial that defines X. This is a classical theme in projective geometry; the central problem is the classification...

Boundary points of the ELSV compactification
Speaker: Bashar Dudin (CMUC)
The celebrated ELSV formula relates the number of covers of the projective line having a given profile over one point and fixed branch points to intersection numbers on the the moduli space of stable marked curves. The former number is essentially of combinatorial nature and boils down to...

Moderate deviations for dependent variables
Speaker: Paulo Eduardo Oliveira (CMUC)
Large and moderate deviations are an important topic in many theoretical or applied statistical areas. We start by a brief overview of large deviations, mentioning the results for dependent variables. A special interest is put for exact convergence rates. After a first quick look at exact...

Explicit Leap-frog DG method for time domain electromagnetic wave propagation
Speaker: Maryam Khaksar Ghalati (CMUC, Univ. Coimbra)
The discontinuous Galerkin time domain methods are now popular and efficient way for the solution of wave propagation problems. The motivation of modeling scattered electromagnetic wave propagation through the human eye’s structure brings us to solving aMaxwell’s equations with...

Nonlinear propagation of waves of short wavelength in dispersive systems
Speaker: Sílvio Gama (Univ. Porto)
We discuss the nonlinear propagation of waves of short wavelength in dispersive systems and we present the simplest nonlinear short-wave dynamics: $u_{tx} = u - 3 u^2$. We present an algorithm to integrate numerically this equation for periodic and non-periodic boundary conditions. We also...

Medical image processing using the image derivatives
Speaker: Alberto Gambaruto (Barcelona Supercomputer Center, Spain)
Medical image processing remains an active field of research principally due to the difficulty of defining the problem. The most successful approaches are related to solving PDEs that model anisotropic diffusion, where the anisotropy is given spatially by the image gradient or Laplacian,...

Nonlocal models for image processing: properties and applications
Speaker: Eduardo Cuesta (Univ. Valladolid, Spain)
One of the alternatives for the mathematical formulation of image processing problems is based on local, nonlinear PDEs models. In the first part of the talk, a brief overview of them, with special regards to morphological and structural properties, will be done. In the second part, some...

Gangster operators and invincible positive semi-definite matrices
Speaker: Charles R. Johnson (The College of William & Mary, USA)
In the relatively new subject of semidefinite programming, positive definiteness plays the role of scalar positivity and inequalities in the PSD partial order replace standard inequalities, relative to linear programming. The subject hashad great success in solving or approximately solving...

On the numerical approximation of algebraic equations with symmetries
Speaker: Angel Durán (Univ. Valladolid, Spain)
The resolution of systems of algebraic equations with symmetry groups appears in the mathematical treatment of many models, [1, 2]. These groups consist of transformations that map solutions of the algebraic system into other solutions. Some consequences of the existence of such symmetry...

Trigroups and M-theory
Speaker: John Huerta (CMAGDS, IST, Lisboa)
A trigroup is a tricategory with one object and all 1-, 2- and 3-morphisms invertible. M-theory is a mysterious branch of physics believed to unify the five 10D string theories and 11D supergravity. Without assuming any knowledge of physics, we will describe how the mathematics of M-theory...

Pattern formation on evolving biological surfaces: the surface fi nite element method applied to reaction-diff usion systems
Speaker: Raquel Barreira (IP Setúbal)
The abstract is in the attached pdf file...

Semisimple Hopf algebra actions
Speaker: Christian Lomp (Univ. Porto)
We review Hopf algebra actions on rings with particular emphasis on a question raised by Miriam Cohen in 1985 whether the smash product A\# H of a semisimple Hopf algebra H acting on a semiprime algebra A is itself a semiprime ring. This question is open until now. In my talk I give a...

Growth and periodicity in representation theory
Speaker: Karin Erdmann (Univ. Oxford, UK)
We consider finite-dimensional modules of finite-dimensional algebras. Any such module has a (unique) minimal projective resolution, that is, a resolution where terms are direct summands of free modules, as small as possible. One would like to know its rate of growth, known as the...

The geometry and topology of random simplicial complexes.
Speaker: Armindo Pereira da Costa (Univ. Warwick, UK)
In this talk we will explore the topological features of random simplicial complexes. We will introduce two models that extend the Erdős–Rényi model for generating random graphs. Unlike in the one-dimensional case (random graphs), we may...

A parabolic Harnack inequality for a nonlocal in time diffusion equation
Speaker: Juhana Siljander (Univ. Helsinki, Finland)
Nonlocal PDEs have gathered a lot of interest during the last years. In particular, the fractional Laplacian and its generalizations have been studied extensively recently. In this talk we will discuss a different kind of nonlocal equation: namely a parabolic diffusion model where the ...

Weighted Sobolev orthogonal polynomials on the unit ball
Speaker: Miguel Piñar (Univ. Granada, Spain)
For the classical weight function on the unit ball, a Sobolev inner product involving the gradient operator is considered. For this inner product a family of mutually orthogonal polynomials on the unit ball is constructed in terms of spherical harmonics and a sequence of Sobolev orthogonal...

On Chow stability for algebraic curves
Speaker: Hugo Torres Lopez (CIMAT, Mexico)
In the last decades there have been introduced different concepts of stability for proyective varieties. In this talk we recall the Chow stability introduced by Mumford for projective varieties, and we prove a natural and intrinsic criterion of the Chow stability for irreducible smooth...

Normality and its weaker forms
Speaker: Mack Matlabyana (Univ. of Limpopo, South Africa)
In this talk we characterize normality and the weaker variants of normality by some quotient maps, namely, uplifting quotient maps, C1-quotient maps, R*- and G*-quotient maps....

Normal semicontinuous functions in pointfree topology and weak cb-frames
Speaker: Imanol Mozo Carollo (Univ. of the Basque Country, Bilbao, Spain)
In a recent paper [2], we have constructed the Dedekind completion of the lattice C(L) of continuous real functions on a frame L, in terms of normal semicontinuous functions. Of course, this construction evokes the classical description of the completion of C*(X) (bounded continuous real...

Generalized Bargmann transforms attached to Landau levels
Speaker: Zouhair Mouayn (Univ. Coimbra)
We construct a family of generalized Bargmann transforms mapping isometrically the states Hilbert spaces of specific Hamiltonian operators onto  L2-eigenspaces associated with Landau levels of a uniform magnetic field on the Euclidean plane, the Poincaré disk and the Riemann...

Educational interfaces between Mathematics and Industry. Report on an ICMI-ICIAM Study.
Speaker: Rudolf Strässer (J.L. Univ. Giessen, Germany & A.C. Univ. Brisbane, Australia)
The presentation will offer some results of the joint ICMI-ICIAM-study on "Educational Interfaces between Mathematics and Industry (EIMI)", which finished in 2013. Elaborating on Mathematics in these different institutions, it will briefly present the role of...

Hermitian matrices and Hodge numbers of irregular algebraic surfaces
Speaker: Margarida Mendes Lopes (IST/UL)
In this talk it will be explained how properties of spaces of hermitian matrices can be used to obtain lower bounds for the h^1,1 Hodge number of irregular algebraic surfaces and in particular to show the non existence of surfaces with certain invariants. After a brief explanation of the...

Universality laws for time-frequency ensembles
Speaker: Luís Daniel Abreu (ARI-Austrian Acad. of Sciences)
There is a transdisciplinar idea known as "Universality" which aims to understand how the macroscopic laws of nature can be obtained from those ruling the microscopic world. The following phenomenon seems to be pervasive: often, a system of interacting objects (for instance,...

Taylor property revisited
Speaker: Joana Leite (CMUC and Instituto Politécnico de Coimbra, ISCAC)
Empirical properties systematically observed in time series of a certain field play an important part in scrutinizing models, as models proposed for them should be able to reproduce these, so called, stylized facts. The Taylor effect is a stylized fact regarding the autocorrelation...

On special class of para-orthogonal polynomials
Speaker: Kenier Castillo (Univ. Estadual Paulista, Sao Paulo, Brazil)
We study the zeros in connection with perturbed recurrence coefficients of polynomials satisfying a certain three-term recurrence relation.   As a particular case, we consider the Askey para-orthogonal polynomials on the unit circle, ${_2}F_1(-n, a+b i; 2 a; 1-z)$, $a,b \in \re$,...

Virial Theorem in Lagrangian formalism
Speaker: Patrícia Santos (CMUC/ISEC)
In this talk the geometric approach to the virial theorem in Lagrangian formalism is presented in quasi-velocities, and a generalization of the virial theorem on Lie algebroids is given. The virial theorem was introduced by Clausius in statistical mechanics in 1870 and since then it became...

Monoids and pointed S-protomodular categories
Speaker: Andrea Montoli (CMUC, Univ. Coimbra)
We investigate the notion of pointed S-protomodular category, with respect to a suitable class S of split epimorphisms, and we show that these categories satisfy, relatively to the class S, many partial aspects of the properties of Mal'tsev and protomodular categories, like the split short...

Geodesic paths and weakly Mal'tsev categories
Speaker: Nelson Martins Ferreira (CDRSP, ESTG, IP Leiria)
We introduce an algebraic structure with the purpose of modelling an arbitrary space with a suitable notion of geodesic path for every two points in it. We prove that this structure satisfies a weak Mal'tsev property, and show that any smooth surface in which every two points are linked by a...

Wasserstein metric and seismic exploration
Speaker: Bjorn Engquist (Univ. of Texas at Austin, USA)
In seismic exploration a wave field is generated at the surface and reflections from the earths interior are recorded. The purpose is to find properties such as wave velocity and location of reflecting sub layers. This can be in an inverse problem where the ...

Non local phase transitions
Speaker: Yannick Sire (Univ. d'Aix-Marseille, France)
I will describe a few recent results dealing with the Allen-Cahn equations with a fractional laplacian. The results are in connection with a fractional version of a conjecture by De Giorgi. I will also explain several open problems and what is the state of the art....

Orthogonal polynomials associated with Laguerre weight matrix
Speaker: Nikta Shayanfar (K. N. Toosi Univ. of Technology, Tehran, Iran)
We study a sequence of matrix polynomials (Pn)n of size nxn, which are orthogonal with respect to the weight matrix involving the classical Laguerre scalar weight.  This family of orthogonal matrix polynomials satisfy a second order differential equation with coefficients ...

Sums of squares on the hypercube
Speaker: João Gouveia (CMUC/Univ. Coimbra)
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of squares of rational functions modulo the vanishing ideal I(X). We are interested in the existence of rational function representations of small degree. We will show how to derive a general...

Surfaces with p_g=0, K^2=3 and 5-torsion
Speaker: Carlos Rito (Univ. Porto)
There is (almost) no information available on the literature about complex algebraic surfaces of general type with geometric genus pg=0, self-intersection of the canonical divisor K2=3 and with 5-torsion.If S is a quintic surface in P3 having 15 3-divisible ordinary cusps as only...

Bullwhips, conservation laws and 1-Laplacian
Speaker: Dmitry Vorotnikov (CMUC, Univ. Coimbra)
We study the equation of motion for inextensible strings with the "whip" boundary  conditions. We prove existence of generalized Young measure solutions after  transforming the equation into a system of conservation laws and approximating it with a regularized system...

GLODS: Global and Local Optimization using Direct Search

Ana Luísa Custodio (Univ. Nova de Lisboa, Portugal)

Locating and identifying points as global minimizers is, in general, a hard and time-consuming task. Difficulties increase when the derivatives of the functions defining the problem are not available for use. In this talk, we propose a new class of methods suited for global derivative-free...

Combinatorial Game Theory: a survey
Speaker: Carlos Pereira dos Santos (ISEC)
In the first years of the 20th century the analysis of the game of nim (by the mathematician Charles L. Bouton) triggered the outburst of a completely new mathematical subject: Combinatorial Game Theory. The aim of this seminar is to give a survey of the development of this mathematical...

On the Gromov width of polygon spaces
Speaker: Alessia Mandini (Univ. of Pavia, Italy)
After Gromov' foundational work in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold (M,\omega) is a symplectic invariant that measures, roughly speaking, the size of the biggest ball we can symplectically embed in...

A Cohen type inequality for Laguerre-Sobolev expansions
Speaker: Maria Francisca Perez Valero (Univ. Carlos III, Madrid, Spain)
In the framework of approximation theory, a Cohen type inequality is a lower bound for the norm of the partial sums of the Fourier expansions in terms of a certain orthogonal system. This kind of inequalities have been investigated by many authors in various contexts and forms, including...

2A-replication and the Baby Monster
Speaker: Rodrigo Farinha Matias (CMUC, Univ. Coimbra)
In the first half of this seminar we will make an introduction to "Moonshine". Namely, we will talk about modular forms, Hecke operators, the Monster Group, Kac-Moody-Lie algebras, vertex algebras, replicability of power series and how these structures are all interrelated to each...

Attractors of trajectory spaces in fluid mechanics
Speaker: Stanislav Kondratyev (CMUC, Univ. Coimbra)
It often happens in fluid mechanics that initial and boundary value problems are not known to be uniquely solvable.  In this case the dynamics can be appropriately treated in terms of trajectory spaces.  The talk will review a few concepts of attractors applicable to trajectory...

Derivatives for equational theories and a special case of Taylor's conjecture
Speaker: Luís Sequeira (CAUL, Univ. Lisboa)
The theory of Maltsev conditions has provided many useful characterizations of properties of varieties, like permutability or modularity of congruence lattices, by the satisfaction of certain identities. The notion of "derivative" for a  an equational theory (or, equivalently,...

The set of equational classes of finitary functions on a finite set as a profinite semigroup
Speaker: Jorge Almeida (CMUP, Univ. Porto)
For a fixed finite set A, we consider sets of finitary functions (or operations) on A, henceforth called classes. We are interested in such classes that can be defined by certain functional equations. It turns out that they constitute a semigroup under the natural notion of class...

Numerical solution of Sturm--Liouville problems via Fer streamers
Speaker: Alberto Gil C. P. Ramos (Univ. Cambridge, UK)
We address the numerical challenge of solving Sturm-Liouville problems in Liouville's normal form, with regular boundary conditions and a continuous and piecewise analytic potential. The novelty of our approach, which is based on a non-standard truncation of Fer expansions, which we call...

On closure properties of some risk aversion measures
Speaker: Nuria Torrado-Robles (CMUC, Univ. Coimbra)
Increasing risk aversion (IRRA) is a common assumption in economics, but this property often is difficult to verify. In this talk, we provide alternative characterizations of IRRA utility functions in terms of increasing absolute risk aversion (IARA) utility functions. We also present some...

The symmetrization problem in the theory of multiple orthogonal polynomials
Speaker: Edmundo Huertas Cejudo (CMUC, Univ. Coimbra)
For a symmetric sequence of type II multiple ortogonal polynomials satisfying a high-term recurrence relation, we provide the relationship between the Weyl function associated to the corresponding block Jacobi matrix and the Stieltjes matrix function. Next, from an arbitrary (and not...

Rainbow connection in graphs
Speaker: Henry Liu (Univ. Nova de Lisboa)
For a connected graph G, the rainbow connection number rc(G) is the minimum number of colours required to colour the edges of G so that, any two vertices are connected by a "rainbow" path (i.e., using distinct colours). The function rc(G) was introduced by Chartrand, Johns, McKeon...

Supercharacters, non-commuting symmetric functions and set partition combinatorics
Speaker: Carlos André (Univ. Lisboa)
The representation theory of the symmetric group is a fundamental model in combinatorial representation theory because of its connections to partition and tableaux combinatorics. It has become clear in recent years that the super-representation theory of the finite unitriangular group has a...

Financial risk measures
Speaker: Miguel Mendes (FEUP/CMUP, Univ. Porto)
We review the concept of risk measure and its use as a capital requirement in the financial industry or as a premium in the insurance context. We then consider the Choquet integral as an important representation of risk measures and specialise to distortion risk measures. Our main innovation...

Dynamics and interpretation of some integrable systems via orthogonal polynomials
Speaker: Amílcar Branquinho (CMUC, Univ. Coimbra)
We establish the correspondence between a non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair. We study the solution of the discrete dynamical system, giving explicit expressions for the resolvent function associated with...

Mathematical modelling of Angiogenesis -flow, elasticity and experiments
Speaker: Rui Travasso (Center for Computational Physics, Univ. Coimbra)
Understanding angiogenesis in a pathological setting is a challenging problem with important consequences for diagnosis and treatment of severe diseases such as cancer. We present a multi-scale phase- field model that combines the benefi ts of continuum physics description and the capability...

Codes over a weighted torus
Speaker: Jorge Sentieiro Neves (CMUC, Univ. Coimbra)
We will describe a new family of linear codes, extending the notion of projective generalized Reed-Muller codes to a setting where the grading of the polynomial ring is non-standard. We will show how the invariants of the numerical semigroup generated by the weights of the variables come...

Essential spectrum for graphs of radial functions
Speaker: Fábio Montenegro (UFC, Brazil)
We prove that if M is a complete hypersurface in R^{n+1} which is the graph of a real radial function, then the spectrum of the Laplace operator on M is the interval [0, \infty)....

On the weak-approximate fixed point property
Speaker: Cleon Barroso (UFC, Brazil)
In this talk we will present a research line known as weak-approximate fixed point property. Some related problems and contributions will be addressed. We will also present some interesting applications related to the fixed point theory, and also to the theory of ordinary differential...

On the contributions of lattice theory to the study of persistent homology.
Speaker: João Pita Costa (Josef Stefan Institute, Liubliana, Slovenia)
In the past 20 years Topological Data Analysis has been a vibrant area of research a lot due to the developments in applied and computational algebraic topology. Essentially it applies the qualitative methods of topology to problems of machine learning, data mining or computer vision. Under...

Geometric Quantum Mechanics and applications
Speaker: Jesús Clemente-Gallardo (Univ. Zaragoza, Spain)
We can notice that the approaches to Classical and Quantum Mechanics are quite different in many aspects, the most striking one being the linear structure which is present in the Hilbert space H and which is considered usually as one of the most relevant aspects of the formalism. There are...

Optimal control applications in blood flow simulations
Speaker: Jorge Tiago (IST, Lisboa)
Blood flow simulations can be improved by integrating known data into the numerical simulations. Data assimilation techniques based on a variational approach can have an important role on this. We will introduce a nonlinear optimal control problem to reconstruct a blood flow profile from...

Some recent developments of a non-dissipative DGTD method for time-domain electromagnetics
Speaker: Stéfane Lanteri (INRIA Sophia Antipolis-Méditerranée)
Nowadays, a variety  of modeling  strategies exist for the computer simulation of electromagnetic wave propagation in the time domain. Despite a lot of advances on numerical methods able to deal accurately and in a flexible way with complex geometries through the use of...

Boundedness for some doubly nonlinear parabolic PDEs
Speaker: Eurica Henriques (CM/UTAD)
We show that, in the setting of measure spaces equipped with a doubling non-trivial Borel measure $\mu$, of dimension $d_\mu$, supporting a weak Poincaré inequality, the nonnegative weak subsolutions of the doubly nonlinear equation $(u^{q})t-\div{(|\nabla u|^{p-2}\nabla u)}=0, ...

Obstacle problems in variable exponent Sobolev spaces
Speaker: Rafayel Teymurazyan (CMAF, Univ. Lisboa)
We are going to discuss the obstacle problem for a quite large class of heterogeneous quasi-linear degenerate elliptic operators in variable exponent Sobolev spaces (Orlicz-Sobolev spaces). We see that the solution has C^{1,\alpha}_{loc} regularity for some \alpha\in (0,1) and prove...

Einstein manifolds with skew torsion
Speaker: Ana Cristina Ferreira (Univ. Minho)
In this talk, we will present a systematic investigation of manifolds that are Einstein for a connection ∇ with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any Einstein manifold with skew torsion has...

What is a tensor product internally?

Tim Van der Linden (Université Catholique de Louvain, Belgium)

When the concept of tensor product is studied from a categorical perspective, it is usually treated either as additional structure on a category - which leads to the theory of monoidal and enriched categories - or in an ad-hoc way involving free algebras of some kind. Quite surprisingly, as...

Remarks on reflexive multiplicative graphs in Gumm categories
Speaker: Diana Rodelo (CMUC and Univ. Algarve)
A Gumm category is a finitely complete category where the categorical version of the Shifting Lemma holds. In varieties of universal algebras, the validity of this lemma is equivalent to being congruence modular. Mal'tsev and Goursat categories give examples of Gumm categories. We show that...

Experimental Optimization: the elephant in the room
Speaker: Bunin Gene (EPFL, Lausanne, Switzerland)
Experimental optimization problems, though ubiquitous in the applied sciences, are a surprisingly underdeveloped field from the theoretical perspective. In this talk, we will define a canonical experimental optimization form, show how it is a generalization of the better-known...

Gray codes and lexicographical combinatorial generation for nonnesting and sparse nonnesting set partitions
Speaker: Alessandro Conflitti (CMUC, Univ. Coimbra)
I shall discuss about combinatorial Gray codes and explicit designs of efficient algorithms for lexicographical combinatorial generation of the sets of nonnesting and sparse nonnesting set partitions of length n and type A....

Modelação e monitorização de dados usando famílias de distribuições
Speaker: Fernanda Otília Figueiredo (Fac. Economia, Univ. Porto)
A utilização de famílias de distribuições na modelação de dados reais permite uma maior versatilidade na escolha do modelo que melhor se ajusta às diferentes peculiaridades dos dados. Apesar da desvantagem subjacente à...

A new test for multivariate normality by combining extreme and non-extreme BHEP test statistics
Speaker: Carlos Tenreiro (CMUC/FCTUC)
In this talk we present a new multiple test procedure for assessing multivariate normality which combines the BHEP (Baringhaus-Henze-Epps-Pulley) tests by considering extreme and non-extreme choices of the smoothing parameter figuring in the definition of the BHEP test statistic. The results...

A quantitative Hölder exponent for the non-homogeneous p-parabolic equation
Speaker: José Miguel Urbano (CMUC, Univ. Coimbra)
That weak solutions of degenerate parabolic pdes modelled on the inhomogeneous p-Laplace equation are Hölder continuous is known for almost 30 years. What was hitherto missing from the literature was a precise and sharp knowledge of the Hölder exponent in terms of p, the...

Hermite finite elements for fluid flow and heat transfer
Speaker: Vitoriano Ruas (UPCM-Paris 6, France)
Traditionally Hermite finite elements have been used to solve fourth or higher order boundary value PDE's, for in this case minimum continuity of solution derivatives must be ensured. It turns out that nothing prevents this kind of methods from being used to solve second order boundary value...

On error control and adaptivity for convection-dominated problems
Speaker: Emmanuil H. Georgoulis (Univ. Leicester, UK)
Advection-dominated advection-diffusion-reaction elliptic and parabolic problems are known to be challenging numerically, due to the stiffness created by the interplay between the advection and the diffusion. In the context of finite element methods, a number of techniques which...

A structure theorem for co-Kähler manifolds
Speaker: Giovanni Bazzoni (Universität Hamburg, Germany)
Co-symplectic and co-Kähler structures are the odd-dimensional analogue of symplectic and Kähler structures. In this talk we shall review the basic concepts of both geometries, which are a special case of almost contact metric structures. We will prove a structure theorem for...

Double negation and other sites on monoides of sequences related to the convergence
Speaker: Luis Espanol (Univ. de La Rioja, Logroño, Spain)
The abstract is in the attached pdf file....

The frame of partial reals and the Dedekind order completion of C(L)
Speaker: Imanol Mozo Carollo (Univ. of the Basque Country, Bilbao, Spain)
Let L(R) denote the frame of reals [1], that is, the frame generated by all ordered pairs (p,q) of rationals, subject to the relations(R1) (p,q) ^ (r,s) = (p v r, q ^ s),(R2) (p,q) v (r,s) = (p,s) whenever p <= r < q <= s,(R3) (p,q) =V{(r,s) | p < r < s < q},(R4) V{(p,q) |...

Some basic spectral properties of complex tridiagonal matrices and the one-dimensional perturbations method.

Mikhail Tyaglov (Shanghai University, China)

In the talk we give some properties of the spectrum and the root subspaces of an arbitrary complex tridiagonal matrix. We also consider the related sequences of orthogonal polynomials and study their roots. Finally, we discuss some applications of the one-dimensional perturbations method...

Regularity for anisotropic fully nonlinear integro-differential equations
Speaker: Raimundo Leitão (Univ. Coimbra)
We consider fully nonlinear integro-differential equations governed by kernels that have different homogeneities in different directions. We derive a nonlocal version of the ABP estimate, a Harnack inequality, and interior regularity. We show the estimates are stable as the smallest degree...

Cliques and cut-cliques: formulations and applications
Speaker: Pedro Coimbra (ISCAC, Polytechnic Institute of Coimbra)
A network/graph provides an abstract representation, establishing the relationships among a set of elements. It helps organizing the information and provides an overall view of the underlying system.These structures are being used in a large number of areas and scientific domains, namely in...

Stability of hyperfinite knots
Speaker: Pedro Lopes (IST, Lisboa)
A hyperfinite knot is an attempt to make sense of limits of sequences of knots with increasing crossing number.Given a knot invariant taking values on a complete metric space, we define the following quotient space of equivalence classes of knots: two knots are related if, by definition,...

Free boundary problems and geometric regularity theory
Speaker: Eduardo Teixeira (Univ. Federal do Ceará, Brazil)
I will discuss a new geometric approach to problems related to regularity issues for elliptic and parabolic problems. Motivated by fundamental questions from the theory of free boundary problems, this new set of tools has been shown to be rather efficient in the solution of a number...

Choice and Pointfree Topology
Speaker: Bernhard Banaschewski (McMaster Univ., Hamilton, Canada)
Remarks on the interaction between pointfree topology and certain choice principles, specifically the Axiom of Choice (AC), the Axiom of Countable Choice (ACC), and the Boolean Prime Ideal Theorem (PIT), in connection with the following issues:(1) The equivalence of PIT with certain...

A chromaticity-brightness model for imaging processing in a "u + v" framework
Speaker: Rita Gonçalves Ferreira (IST/CMA)
In imaging processing many important issues arise such as image segmentation, color restoration, and image denoising. A rigorous mathematical analysis is needed to validate the extensive numerical analysis literature in this field, and to open new avenues on image...

A new look to non-Fickian diffusion
Speaker: Elias Gudiño (Univ. Coimbra)
In this talk a non-linear mathematical model to describe absorption phenomena in polymers is proposed. The model is established assuming that the diffusing penetrant causes a deformation which induces a stress driven diffusion and consequently a non-Fickian mass flux. We also present a...

Formal deformations and q-deformations in stage, and Hom-algebras
Speaker: Abdenacer Makhlouf (Univ. de Haute Alsace, France)
In this talk I will provide two point of views for deforming algebraic structures. The first approach is formal deformations introduced by Gerstenhaber for associative algebras, using one parameter formal power series, and then extend to Lie algebras by Nijenhuis and Richardson. It will be...

Non-pointed additive category
Speaker: Dominique Bourn (U. Littoral, Calais, France)
The talk will deal with the study of the different degrees of non-pointed additiveness between Naturally Mal'cev categories (when the fibers of the fibration of points are additive) and essentially affine ones (when any change of base functor with respect with the same fibration is an...

\(3\times 3\) matrices with a flat portion on the boundary of the numerical range
Speaker: Fatemeh Esmaeili Taheri (CMUC PhD student)
In recent years, many studies have been done on the numerical range of matrices and bounded operators. In this presentation, the set of unitarily irreducible complex 3×3 matrices whose numerical range has a flat portion will be explicitly described and it will show that this set is connected...

A bijection for the convolution of central binomial coefficients
Speaker: Rui Duarte (Univ. Aveiro)
All known bijective proofs for the convolution of central binomial coefficients $\sum_{i+j=n} \binom{2i}{i} \binom{2j}{j} = 4^n$,are based, with some variations, on the count of lattice paths. In this talk we give a new proof of this identity, where $\binom{2 \ell}{\ell}$ is regarded as the...

On trace spaces of 2-microlocal Triebel-Lizorkin spaces with variable integrability
Speaker: Helena Gonçalves (PhD student)
In this seminar we study the traces of 2-microlocal Triebel-Lizorkin spaces with variable integrability on hyperplanes. Following [2], we present the definition and properties of those spaces, in particular the characterization by atomic decomposition and embedding assertions, needed to...

Some semigroup-theoretic aspects of Rauzy graphs of subshifts

Alfredo Costa (CMUC/Univ. Coimbra)

Symbolic dynamical systems, also called subshifts, correspond in a natural way to factorial prolongable languages. In this context, it is often relevant to study factor graphs, sometimes called Rauzy graphs, to which one gives a natural automaton structure. In this talk we first discuss the...

Categories of lax algebras: a first approach
Speaker: Pier Giorgio Basile (PhD student)
Following the paper of M.M. Clementino and D. Hofmann [2], and having as starting point Barr's description of topological spaces as lax algebras for the ultrafilter monad [1], I am going to present the categories of lax algebras. They represent a suitable generalization of the relational...

Weak solvability of one model of dynamics of thermoviscoelastic continuous medium with regularized objective Jaumann derivative
Speaker: Victor Zvyagin (Voronezh State Univ., Russia)
In the talk, we establish the weak solvability of the initial–boundary value problem for the model of dynamics of thermoviscoelastic continuous medium which rheological relations (constitutive laws) contains regularized objective Jaumann’s derivative. The investigation is carried...

Structures on line bundles - The deRham and Dolbeault grupoids
Speaker: Artur Araújo (PhD student)
Brief introduction to connections and complex structures on a trivial line bundles. Deformation theories; the action of gauge transformations, and the deRham grupoid. Holomorphic structures on a line bundle, and relation to connections. Higgs fields, and the Dolbeault grupoid. Equivalence of...

Every prespectrum represents a homology theory
Speaker: Fernando Lucatelli (PhD student)
Eilenberg and Steenrod proved that ordinary homology is characterized by five axioms. Later, Atiyah, Hirzebruch and Whitehead observed that there are other families of functors that satisfy the four "most important" axioms. They defined the so called "generalized homology...

Riesz and Wolff potentials in variable exponent Lebesgue spaces
Speaker: Alexandre Almeida (Univ. Aveiro)
We study mapping properties of Riesz and Wolff potentials in Lebesgue spaces with variable exponent. Our approach includes the limiting case corresponding to potentials of L1 functions. This case is particularly interesting in the study of some nonlinear PDEs. ...

Classification of quadratic Lie algebras of low dimension
Speaker: Said Benayadi (Univ. de Lorraine, France)
In this talk we give the classification of the irreducible non solvable Lie algebras of dimension less than or equal to 13 with nondegenerate, symmetric and invariant bilinear forms....

On the structure of graded Leibniz algebras
Speaker: José M. Sánchez Delgado (Univ. Malaga, Spain)
We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field. We show that any of such algebras with a symmetric G-support is the sum of a subspace of L_1 (the homogeneous component associated to the unit element 1 in G) with a family of I_j, a...

(1,1)-Coherent pairs on the unit circle
Speaker: Natalia Camila Pinzón Cortés (Univ. Carlos III, Madrid, Spain)
see file...

Modular classes and Dirac structures
Speaker: Raquel Caseiro (CMUC/Univ. Coimbra)
We begin by reviewing some properties concerning modular classes in Poisson and Lie algebroid theory. By generalizing modular classes to Dirac structures, we have a general framework to understand these structures and the reduction example of a Poisson manifold become more clear....

Quaternion arithmetic: factorization and geometry
Speaker: António Machiavelo (CMUP/Univ. Porto)
The ring of the so called Hurwitz integers, which contains the integral quaternions, being both a left and a right PID, is the appropriate ring inside the quaternions in which to study arithmetical questions. The fact that it is a non commutative ring entails some complications, but also...

On quasi-étale quotients of products of two curves
Speaker: Roberto Pignatelli (Univ. degli studi di Trento, Italy)
I will consider finite groups acting on the products of two complex algebraic curves freely out of a finite set of points. Geometrically, this means that the map onto the quotient is quasi-étale. I will describe some results obtained in the last few years by several authors including...

Sylvester equations for Laguerre-Hahn orthogonal polynomials on the real line
Speaker: Maria das Neves Rebocho (Univ. Beira Interior/CMUC)
The main purpose of the talk is to introduce matrix Sylvester differential equations in the study of Laguerre-Hahn orthogonal polynomials.It is shown an equivalence between the scalar Riccati differential equation for the Stieltjes function and matrix Sylvester differential equations for...

On Besov and Triebel-Lizorkin-type spaces
Speaker: Susana Moura (CMUC/Univ. Coimbra)
We give a survey on Besov and Triebel-Lizorkin spaces, from classical to 2-microlocal spaces with variable integrability. Embeddings and traces will be considered....

Coherent states quantization and formulae for the Berezin transform
Speaker: Zouhair Mouayn (Univ. Sultan Moulay Slimane, Morocco)
We are concerned with bound states eigenspaces of the Schrodinger operator with magnetic field in Cn and in the complex unit ball Bn. We construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover...

Infinitesimally injective polynomial modules
Speaker: Steve Donkin (Univ. of York, UK)
Working over a field of positive characteristic, we consider the problem of describing, by highest weight, the injective polynomial injective modules for the general linear group GL(n) which are also injective as restricted modules for the general linear Lie algebra gl(n). This is equivalent...

Experiments with numerical semigroups
Speaker: Manuel Delgado (CMUP/Univ. Porto)
A set of natural numbers that is closed under addition and whose complement in the set of non negative integers is finite is said to be a numerical semigroup. The number of positive integers not belonging to a numerical semigroup is said to be its genus. Question: How many numerical...

On the Beck-Chevalley condition for Set-monads
Speaker: Maria Manuel Clementino (CMUC/Univ. Coimbra)

Automatic presentations for algebraic and combinatorial structures
Speaker: Alan J. Cain (Univ. Porto)
An automatic presentation (also called an FA-presentation) is a description of a relational structures using regular languages. The concept of FA-presentations arose from computer scientists' need to extend finite model theory to infinite structures. Informally, an FA-presentation consists...

An introduction to Sasakian geometry
Speaker: Antonio De Nicola (CMUC)
I will introduce the first elements of contact and almost contact geometry, starting from the notion of contact manifold. I will briefly mention its relation with symplectic geometry as well as some application to physics. Finally, I will present the notions of normality and compatible...

Stability of heteroclinic networks
Speaker: Sofia Castro (Fac. Economia, Univ. Porto)
Invariant sets are important objects in the study of dynamical systems since they allow us to describe families of trajectories/solutions. In fact, a solution starting in an invariant set will remain in this set for all time. Whether this solution is complex...

Fickian diffusion versus non Fickian diffusion in porous media
Speaker: José Augusto Ferreira (CMUC/Univ. Coimbra)
Traditionally, diffusion process in porous media are described by convection-diffusion-reaction equations established using Fick's law for the mass flux. Such equations give accurate results in laboratory environment for perfectly homogeneous media. Nevertheless when nonhomogeneous media...

Derivatives of functions of matrices
Speaker: Pedro J. Freitas (Univ. Lisboa)
There have been recent results concerning directional derivatives, of degree higher than one, for the determinant, the permanent, the symmetric and the antisymmetric power maps, by R. Bhatia, P. Grover and T. Jain. We present generalizations of these results for immanants and other symmetric...

A Cauchy kernel expansion and Fomin's growth diagrams.
Speaker: Aram Emami (CMUC)
We give a bijective proof of a Lascoux's Cauchy kernel expansion over Ferrers shapes, in two families of Demazure operators. The proof is given in the framework of Fomin's growth diagrams for generalized Robinson-Schensted-Knuth correspondences, in our case, to obtain pairs of semi-skyline...

Dirac structures
Speaker: Raquel Caseiro (CMUC/Univ. Coimbra)
Dirac structures were introduced by T.Courant and A. Weinstein as a way to unify pre-symplectic and Poisson geometry. We intend to present the basics of Dirac structures, including main geometric features and key examples. First we introduce linear Dirac structures and then we generalize...

Special completions of semilattices and lattices
Speaker: Maria João Gouveia (Univ. Lisboa)
Canonical extensions of (bounded) lattices have been extensively studied, and the basic existence and uniqueness theorems for these have been extended to general posets. In this talk we will consider profinite completions of semilattices which may be identified with the iterated filter...

Sublattices of associahedra and permutohedra equations satisfied by associahedra
Speaker: Luigi Santocanale (Univ. de Provence, France)
The set of permutations on n-elements is a poset when endowed with weak Bruhat ordering.  Actually, this poset is a lattice since each finite subset of permutations has both a supremum and infimum. Such a lattice is known as the Permutohedron on n-elements. A strictly related lattice is...

Zero behavior of certain perturbed ortogonal polynomials
Speaker: Edmundo Huertas Cejudo (Univ. Coimbra)
This talk is focused in the so called canonical spectral transformations of measures. We analyze the behaviour of zeros of MOPS associated with the Christoffel and Uvarov transformations of the measures. First, we introduce the representation of the perturbed MOPS in terms of the initial...

Hom-Lie algebroids
Speaker: Joana Teles (CMUC/Univ. Coimbra)
We review some definitions and constructions of hom-Lie algebras, hom-associative algebras and hom-Poisson algebras. We define hom-Lie algebroids, a definition that may seem cumbersome at first, but which is justified, first, by a one-to-one corespondence with hom-Gerstenhaber algebras, a...

A short introduction to Coxeter systems through combinatorics of words
Speaker: Alessandro Conflitti (CMUC/Univ.Coimbra)
We give an introduction to abstract Coxeter systems using a combinatorial approach based on words, thus avoiding all the original geometric framework. The talk will be self contained, assuming no previous knowledge or background, save for very basic algebra....

Eigenvalue complementarity problem: applications and algorithms
Speaker: Luís Merca Fernandes (IP Tomar/IT)
The Eigenvalue Complementarity Problem (EiCP) finds important applications in different areas of science and engineering and differs from the traditional Eigenvalue Problem on the existence of nonnegative constraints on its variables and complementarity constraints between pairs of...

Regularity for some doubly nonlinear evolutionary equations in measure spaces
Speaker: Rojbin Laleoglu (CM, Univ. Trás-os-Montes e Alto Douro)
We will consider the regularity question for the nonnegative weak solutions of certain doubly nonlinear parabolic equations falling into a very large and important class of equations, namely the class of degenerate and singular equations. These type of evolutionary equations appear in the...

Monochromatic Kr-decompositions of graphs
Speaker: Teresa Maria Jerónimo Sousa (Univ. Nova de Lisboa)
Given graphs G and H, and a colouring of the edges of G with k colours, a monochromatic H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a monochromatic graph isomorphic to H. Let $\phi_{k}(n,H)$ be the smallest number t, such that...

On Alexander's Subbase Lemma
Speaker: Dirk Hofmann (U. Aveiro)
Alexander's Subbase Lemma (due to James Waddell Alexander II) is a classical result of topology stating that a topological space X is compact provided that X is compact with respect to a subbasis, that is, every subbasic cover of X has a finite subcover. In this talk we will give a very...

Linear potentials in nonlinear potential theory
Speaker: Tuomo Kuusi (Aalto Univ., Helsinki, Finland)
We give an update to some aspects of the theory for solutions to nonlinear elliptic or parabolic, possibly degenerate, equations involving p-Laplacean type operators and datum, which, in full generality, can be a measure. The main focus is to describe recent pointwise potential estimates for...

On multi-objective sequence alignment: formulation and algorithms
Maryam Abbasi (DEI, Univ. Coimbra)
Sequence alignment is used to identify regions of similarity that may indicate functional, structural and/or evolutionary relationships between two or more biological sequences. Usually, the quality of an alignment is given by a score function that is a weighted sum of several components,...

Schreier graphs of self-similar groups
Speaker: Daniele D'Angeli (Univ. Trás-os-Montes e Alto Douro)
Self-similar groups are described as groups acting by automorphisms on a rooted tree and have been used to find examples of groups with special and exotic properties. Schreier graphs naturally appear in this context as orbital graphs of the action on the levels of the tree. In this talk I...

Modeling non-Fickian diffusion processes
Speaker: Elias Gudiño (CMUC)
An important problem in controlled release technology is the diffusion of a penetrant into a polymeric carrier where a drug is dispersed. A suitable choice for simulating drug delivery can be the classical Fick’s law. However to model the sorption of the liquid agent an equation that...

Instantons on the manifolds of Bryant and Salamon
Speaker: Andrew Clarke (IME/USP, Brazil)
The first examples of complete manifolds of holonomy G2 were constructed by Bryant and Salamon in the 1980's. More recently, gauge theory on manifolds on reduced holonomy has be introduced and greatly developed. I will explain this theory in the case of G2 holonomy and explain a new...

Representations and combinatorics related to the Weyl algebra
Speaker: Samuel Lopes (Univ. Porto)
We consider the multiplication and differentiation operators x and d/dx, which generate the Weyl algebra. Fix a nonzero polynomial h=h(x) and let y be the operator h.d/dx, so that x and y satisfy the commutation relation [y, x]=h. The algebra generated by x and y is denoted by A_h and is a...

KAM and presymplectic dynamics
Speaker: Hassan Alishah (IST, Lisboa)
Classical Kolmogrov-Arnold-Moser theory studies stability problem for invariant tori for nearly integrable dynamical systems. This theory has been developed beyond nearly integrable systems. I will explain basic concepts and results of the classical KAM theorem. Then I will state a KAM...

Multiscale analysis in hydrodynamics
Sílvio Gama (Univ. Porto)
This seminar will start with a brief introduction to multiscale techniques. Afterwards, we will use these techniques to derive the large scale transport coefficients (eddy viscosity tensor included), as well as the equations that govern the large-scale dynamics. Time permitting, some results...

Algebras, monoidal structures and cocycles
Speaker: Dimitri Chikhladze (CMUC)

Dirichlet problem in a domain with a small hole
Speaker: M. Dalla Riva (CIDMA, Univ. Aveiro)
We consider a Dirichlet problem in a domain with a small hole of diameter proportional to a real parameter $\epsilon$ and we denote by $u_\epsilon$ the corresponding solution. We show that the behavior of $u_\epsilon$ for $\epsilon$ small and positive can be described in terms of real...

Vector bundles over Lie groupoids and Lie algebroids
Speaker: Matias del Hoyo (IST, Lisboa)
In a real vector space addition is settled by scalar multiplication. This makes possible to describe smooth vector bundles as manifolds endowed with a nice action of the multiplicative monoid of the real numbers. In this talk I will deal with vector bundles over Lie groupoids and algebroids....

Recent developments in matrix pencils completion problems
Speaker: Marija Dodig (CELC, Univ. Lisboa)
In this talk we shall present some new results on matrix pencil completions. The common point of all of them is a purely combinatorial problem involving triples of partitions. We shall show a solution to the combinatorial problem and give various examples of its  applications to matrix...

On difference-differential equations for deformed Laguerre-Hahn orthogonal polynomials on the unit circle
Speaker: Amílcar Branquinho (CMUC, Univ. Coimbra)
In this talk we study sequences of orthogonal polynomials on the unit circle whose Carathéodory function satisfies a Riccati-type differential equation with polynomial coefficients. We deduce discrete Lax equations which lead to difference equations for the corresponding sequences of...

A meeting point between matroid and representation theory
Speaker: Inês Legatheaux Martins (CELC, Univ. Lisboa)
In this talk, we introduce a matroid invariant known as the rank partition which was defined by J. A. Dias da Silva in 1990. For matroids realizable over the complex numbers, following recent work of A. Berget, we explain how this concept relates matroid theory to the representation theory...

Mathematical models for the simulation of organic optoelectronic devices
Speaker: Luís Morgado (Univ. Trás-os-Montes e Alto Douro)
Organic semiconductors, and in particular the polymeric, are of enormous interest for high-volume and low-cost manufacturing electronics industry, generally referred to as “printed electronics”. Considering that the first organic light-emitting device (OLED) based on low...

A non-polynomial collocation method for fractional differential equations
Speaker: Maria Luísa Morgado (Univ. Trás-os-Montes e Alto Douro)
In this work we are concerned with the numerical approximation of fractional di fferential equations. We will focus on initial and terminal value problems for ordinary di fferential equations of non-integer order. The approach used is based on the equivalence between this kind of...

Variational models for image segmentation
Speaker: Juan Carlos Moreno (CMUC)
In imaging science, texture and multiphase image segmentation are two problems of great interest. The importance of image segmentation models lies in looking for the best representation of an image into meaningful information by partitioning it into well distinguished regions containing some...

On a family of log-concave symmetric unimodal polynomials.
Speaker: José Agapito Ruiz (FC, Univ. Lisboa)
I will show the construction of an interesting family of polynomial sequences out of a suitable expansion of powers of the monomial (xr Ds), where x stands for multiplication by x and D is the usual derivative operator. Two well-known members of this family are the Eulerian polynomials and...

Matrix operations of almost linear complexity for computing eigenpairs of large dimensional problems
Speaker: Paulo Vasconcelos (CMUP)
We consider the numerical solution of a large eigenvalue problem resulting from a nite rank discretization of an integral operator. We are interested in computing a few eigenpairs, with an iterative method, so a matrix representation that allows for fast matrix-vector products is required....

Primitive Groups are rare (but useful)
Speaker: Daniel Pinto (CMUC, Univ. Coimbra)
A hypermap is, in its topological form, a cellular embedding of a connected hypergraph. Hypermaps can be modified by some operations, like duality (the operation that interchanges hypervertices and hyperfaces on oriented hypermaps). The notion of duality index was created to measure how far...

Asymptotic behaviour of a class of regular maps
Speaker: António João Breda D'azevedo (Univ. Aveiro)
Regular maps are triples $(G,a,b)$ consisting of a group $G$ and a pair $(a,b)$ of generators of $G$ (in fact a conjugacy class) being the product $ab$ an involution. A regular map ${\cal M}=(G,a,b)$ is reflexible or chiral according as $\cal M$ is isomorphic or not to its mirror image...

Regularity and geometric estimates for minima of discontinuous and singular functionals
Speaker: Raimundo Leitão (Univ. Coimbra)
This work consists of two parts: In the first part we study nonnegative minimizers of degenerate elliptic functionals for variational kernels that are discontinuous. The Euler-Lagrange equation is therefore governed by a non-homogeneous, degenerate elliptic equation with free boundary...

Smoothing and worst-case complexity for direct-search methods in nonsmooth optimization
Speaker: Nima Garmanjani (Univ. Coimbra)
For smooth objective functions it has been shown that the worst-case cost of direct-search methods is of the same order as the one of steepest descent. Motivated by the lack of such a result in the nonsmooth case, we propose, analyze, and test a class of smoothing...

A derivative-free optimization algorithm with subspace technique
Speaker: Zaikun Zhang (Univ. Coimbra)
We will talk about optimization algorithms that do not use derivatives, namely, derivative-free algorithms. We discuss how to incorporate subspace techniques into this type of algorithms, and present a new derivative-free algorithm with subspace techniques. For the new algorithm,...

An heterogeneous multiscale method for Aberrant Crypt Foci dynamics
Speaker: Giuseppe Romanazzi (CMUC)
Assuming that Aberrant Crypt Foci (ACF) in the colon are consequence of accumulation of abnormal cells we will characterize the dynamics of these cells, in order to describe the evolution of ACF. The colon  will be considered as a periodic spread  structure composed by a crypt and...

Presentation of differential-algebraic systems with delays (DAD) and applications of fractional derivatives to DAD systems
Speaker: Zbigniew Zaczkiewicz (Politechnika Bialostocka, Poland)

Higher analogues of symplectic fibrations
Speaker: Olivier Brahic (IMPA, Rio de Janeiro, Brazil)
Given a differential form defined on the total space of a fibration, we interpret geometrically the equations for it to be closed. We obtain this an elementary model for  higher TFTs, that can be interpreted as parallel transport along surfaces, volumes... Starting from hamiltonian...

Geometric semi-abelian categories
Speaker: George Janelidze (U. Cape Town, South Africa)

Normalizers and algebraic exponentiation
Speaker: James Gray (UNISA, Pretoria, South Africa)
We recall the definition of algebraic exponents and their relationship to centralizers. We show that for action accessible categories the existence of normalizers implies that the category is fiberwise algebraically cartesian closed....

FEM solutions of some Boussinesq-type models for surface water waves
Speaker: Nuno Lopes (CMAF, Univ. Lisboa)
A class of improved Boussinesq-type models to simulate the propagation and generation of nonlinear dispersive waves is presented. The models are derived in order to keep some dispersive characteristics of higher-order ones. Some stability properties of the numerical models are discussed....

Local Hölder continuity for doubly nonlinear parabolic equations

José Miguel Urbano (CMUC/Univ. Coimbra)

We give a proof of the Hölder continuity of weak solutions for the doubly nonlinear parabolic equation in the degenerate case. The analysis discriminates between large scales, for which a Harnack inequality is used, and small scales, that require intrinsic scaling...

Dualities via splitting idempotents
Speaker: Dirk Hofmann (U. Aveiro)
In 1994, R. Rosebrugh and R. Wood showed that the category of complete distributive complete lattices and suprema preserving maps is equivalent to the idempotent split completion of the category of sets and relations; and ten years later they observed that this result is not really...

Even surfaces with genus 4 and bigenus 13
Speaker: Roberto Pignatelli (Università degli studi di Trento, Italy)
In the study of algebraic surfaces, the surfaces of general type form the biggest and most mysterious class. There is no hope to get a complete classification of them but some interesting results can be obtained by fixing some (topological and birational) invariants: the most important are...

Interpolation of uniformly absolutely continuous operators
Speaker: Bohumir Opic (Charles Univ., Prague, Czech Republic)
We develop a method suitable for interpolation of uniformly absolutely continuous operators. We apply this method to establish compactness of operators and embeddings especially in the limiting situations, where the classical interpolation methods fail. We study types of certain ...

On the separability of clusters
Speaker: Jorge Orestes Cerdeira (ISA/UTL)
Separability of clusters is an issue that arises in many different areas, and is often used in a rather vague and subjective manner. We introduce a combinatorial notion of interiority to derive a global view on separability of a set of entities. We develop this approach further to...

Towards a virtual retina - a multidisciplinary approach
Speaker: Miguel Morgado (IBILI/DFUC)

Sampling in 2D: specificities, difficulties and applications
Speaker: José Manuel Rebordão (DF/FCUL)
Sampling strategies are a fundamental part of any measurement process. In the signal framework (one-dimensional, 1D - usually the time), sampling is a well-controlled process. For two (images, 2D) and three (volumes, 3D) spatial dimensions, one is frequently faced with unknown objects or...

Multivariate Sobolev orthogonal polynomials on the ball
Speaker: Miguel Piñar (Univ. Granada, Spain)
Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding the evaluation of derivatives at several points to a measure, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be...

The kinematic reduction and Hamilton-Jacobi equation on skew symmetric algebroids
Speaker: María Barbero Liñán (Univ. Carlos III, Madrid, Spain)
Hamilton-Jacobi theory has strong similarities with kinematic reduction by means of decoupling vector fields of nonholonomic mechanical control systems. We describe that interconnection on a geometric structure called skew-symmetric algebroid, which generalizes the notion...

Hypersymplectic structures on Courant algebroids

Paulo Antunes (CMUC/Univ. Coimbra)

In this talk, we define hypersymplectic structures on Courant algebroids and show that we recover, as particular cases, all the classical results and examples of hypersymplectic structures on Lie algebroids. As on Lie algebroids, we prove a 1-1 correspondence theorem between hypersymplectic...

Receiver Operator Characteristic Curves in the evaluation of medical diagnosis
Speaker: Pedro Oliveira (Instituto de Ciências Biomédicas Abel Salazar, Univ. Porto)
The origin of Receiver Operating Characteristic (ROC) analysis can be traced to the theory of statistical decision making, related to applications in signal detection and psychology and, over the years, has become a powerful tool for measuring diagnostic tests performance in medicine. A...

Riemann Hilbert problems on a Riemann surface and on the complex plane
Speaker: Maria Teresa Malheiro (Univ. Minho)
We study the solvability of scalar Riemann-Hilbert problems relative to a contour on a torus which are equivalent to some matrix Riemann-Hilbert problems in the complex plane. With this purpose a new concept of meromorphic factorization in the torus is introduced and discussed. The results...

Strong discontinuities in the scope of the discrete crack approach
Speaker: Daniel Dias da Costa (Univ. Coimbra)
The use of the discrete crack approach and Nonlinear Fracture Mechanics opened the possibility of accurately modelling fracture behaviour of quasi-brittle materials, such as concrete, mortar and masonry. In this approach, it is assumed that microcracking localises into a surface of...

Endomorphism algebras of some modules for Schur algebras and representation dimension
Speaker: Stephen Donkin (University of York, UK)
This is joint work with H. Geranios. In a recent paper Miemietz and Oppermann show that, for fixed n\geq 2, the representation dimension of the Schur algebra S(n,r) goes to infinity with r, under certain characteristics restrictions. We show that this the result is valid without...

Quadratic symplectic Lie superalgebras and Lie bi-superalgebras
Speaker: Elisabete Barreiro (CMUC/Univ. Coimbra)
Lie bi-superalgebras arise in the theory of quantum mechanical integrable models and are related to the graded classical Yang-Baxter equation. By a triangular Lie bi-superalgebra we mean a Lie bi-superalgebra which co-multiplication comes from an even skew-symmetric solution of the classical...

Integral affine geometry of non-commutatively integrable Hamiltonian systems
Speaker: Daniele Sepe (IST, Lisboa)
In mechanics there are many Hamiltonian systems which admit more integrals of motion (with suitable properties) than degrees of freedom (e.g. the Euler top). These systems are known as superintegrable or non-commutatively integrable and have been studied extensively since the pioneering...

Hausdorff dimension of functions on d-sets
Speaker: António Caetano (Univ. Aveiro)
The sharp upper bound for the Hausdorff dimension of the graphs of the functions in Holder and Besov spaces (in this case with integrability p\geq 1) on fractal d-sets is obtained: \min\{d+1-s,d/s\}, where s\in(0,1] denotes the smoothness parameter. In particular, when passing from d\geq s...

Existence results for non-Newtonian viscous fluid problems with different types of dissipation

Hermenegildo Borges de Oliveira (Univ. Algarve/CMAF)

This seminar aims to investigate the existence of weak and very weak solutions for generalized Navier-Stokes problems.  We will consider different problems that govern distinct flows of incompressible and homogeneous viscous fluids. The analysis will be made mainly for the versions of...

An agency for Mathematics in interaction with enterprises and society in France
Speaker: Christophe Prud'homme (Univ. Grenoble, France)
I will discuss the creation and the first year of existence of the french Agency for Mathematics in Interaction with Enterprises and Society (AMIES) [1]. First I start with the context in which the agency was funded then I present the organisation, its objectives and the tools it provides to...

Mal'cev products and the locality of pseudovarieties of semigroups
Speaker: Ana Paula Escada (CMUC/Univ. Coimbra)
The global of a pseudovariety of semigroups V is the smallest pseudovariety of semigroupoids which contains V, where members of V are viewed as one-vertex semigroupoids. When the global of the pseudovariety V is characterized by properties of the local semigroups of its semigroupoids,...

De Morgan algebras: new perspectives and applications
Speaker: H.P. Sankappanavar (State University of New York/CAUL)
It is well known that Boolean algebras can be defined using only the implication and the constant 0. It is, then, natural to ask whether De Morgan algebras can also be characterized using only a binary operation (implication) -> and a constant 0. In this lecture, I give an affirmative...

Pairs of compatible tensors on Courant algebroids and hierarchies
Speaker: Joana Nunes da Costa (CMUC/Univ. Coimbra)
We show that a Poisson-Nijenhuis structure can be defined on a Courant algebroid as a pair of compatible tensors satisfying several constraints. Other pairs of compatible tensors such as deforming-Nijenhuis and Nijenhuis pairs can also be considered. We construct natural hierarchies of such...

Deformations of Lie groupoids
Speaker: João Nuno Mestre (Utrecht University)
Deformations of Lie groupoids can be studied by means of the intrinsiccohomology that controls them. This approach is related both to thestudy of deformations of Lie group actions by Palais, and to thelinearization theorem for proper Lie groupoids. We obtain a vanishingresult for the...

On polynomial sequences associated to the classical linear functionals and to second order forms
Speaker: Ana Filipa Loureiro (CMUP)
Polynomial sequences generated by integral powers of first and second order differential operators with polynomial coefficients will be under discussion. More precisely, the focus will lie on their connection with well known orthogonal polynomial sequences along with their foremost...

Non-smooth atomic decompositions in function spaces and applications
Speaker: Cornelia Schneider (Univ. Erlangen-Nuremberg, Germany)
We provide non-smooth atomic decompositions for Besov spaces \Bd(\rn), s>0, 0<p,q\leq \infty, defined via differences, with the help of a homogeneity property.The results are used to compute the trace of Besov spaces on the boundary \Gamma of bounded Lipschitz domains \Omega with...

Counting spectral radii of matrices with positive entries
Speaker: Pedro Freitas (CELC/Mat. FCUL)
We will present some results concerning the number of different spectral radii that you can get for matrices with entries in a prescribed finite set of positive integers. This problem is related to a conjecture by Erdös and Szemerédi about sums and products of elements in a...

On Leibniz algebras and Loday algebroids
Speaker: Yvette Kosmann-Schwarzbach (École Polytechnique, France)
We shall briefly review Leibniz algebras and their cohomology. We shall then define Loday algebroids, give examples and outline their supergeometric interpretation, following the 2011 preprint by Grabowski, Khudaverdian and Poncin....

Hyperpolygons and moduli spaces of parabolic Higgs bundles
Speaker: Alessia Mandini (IST, Lisboa)
In this talk I will describe the geometry of the moduli space of polygons and of its hyperkaehler analogue, the so called hyperpolygon space. In particular I will discuss how these spaces are isomorphic to certain moduli spaces of stable, rank-2, parabolic and parabolic Higgs (respectively)...

Complementing comonads
Speaker: Craig Pastro (Kyushu University, Japan)

Monoidal structures
Speaker: Dimitri Chikhladze (CMUC)

Spectral properties of certain tridiagonal k-Toeplitz matrices
Speaker: Renato Álvarez-Nodarse (Univ. Sevilla, Spain)
Motivated by a physical model of a system of quantum oscillators with nonlinear interactions, we study spectral properties of certain matrices which arise as perturbations of some tridiagonal k-Toeplitz matrices. Concretely, we are interested in the spectral properties of...

On the enumeration of connected graphs with specified biconnected components
Speaker: Ângela Mestre (CELC)
We derive a recurrence for the number of connected graphs whose biconnected components are all graphs on the same vertex and edge numbers. The proof uses Abel's binomial theorem and generalizes Dziobek's induction proof of Cayley's formula....

Optimal partition problems involving Laplacian eigenvalues
Speaker: Hugo Tavares (CMAF, Univ. Lisboa)
Given a bounded domain \Omega\subseteq \RN, N\geq 2, and a positive integer m\in \N, consider the following optimal partition problem \inf{ \sum_{i=1}^m \lambdak(\omegai): \omegai \subset \Omega open \forall i, \omegai\cap \omegaj=\emptyset whenever i\neq j},where \lambdak(\omega)...

Semi-skyline augmented fillings and a non-symmetric Cauchy identity in type A
Speaker: Aram Emami (PhD student CMUC)
The well known Cauchy identity is the best characterization of Schur functions that can be derived using the Robinson-Schensted-Knuth (RSK) correspondence. The Cauchy kernel expands as a sum, over all partitions, of products of Schur functions in variables X and Y separately. The RSK...

Network Optimisation with non-deterministic arc parameters: an application to bloodstream object location
Speaker: Deolinda M. L. D. Rasteiro (ISEC)
Abstract: In this talk we propose algorithms which determine the path that minimizes the expected value of a utility function over a dynamic probabilistic network with discrete or continuous real random variables (parameters) associated to each emerging arc. To obtain the optimal dynamic...

Immanant preserving and immanant converting maps
Speaker: Maria Antónia Duffner Monteiro (CELC/Mat. FCUL)
Let Mn be the  algebra of all n-square complex matrices. I will characterize maps φ:Mn→Mn that satisfy: dχ(φ(A)+λφ(B)) = dχ'(A+λB) for all A,B ∈ Mn and every complex number λ; where χ and χ' are arbitrary irreducible...

Mal'tsev categories and a generalised 3x3 Lemma
Speaker: Diana Rodelo (CMUC/Univ. Algarve)
We prove that a regular category C is a Mal'tsev category if and only if a strong form of the denormalised 3x3 Lemma holds true in C....

Shreier Mac Lane theorem in the Mal'cev context
Speaker: Dominique Bourn (Univ. du Littoral, Calais, France)

Enumerative results and poset structure for a class of binary matrices equipped with a generalization of the Bruhat order
Speaker: Alessandro Conflitti (CMUC)
Recently, Brualdi et al. defined a partial order on an interesting class of binary matrices which generalizes the classical Bruhat order on the symmetric group, seen as the set of permutation matrices. We study the structure of this poset, and we give some enumerative results, e.g. about the...

Higher central extensions via binary commutators
Speaker: Tim Van der Linden (Univ. catholique de Louvain, Belgium)
We prove that all semi-abelian categories with the Smith is Huq property satisfy the Commutator Condition: higher central extensions may be characterised in terms of binary (Huq or Smith) commutators. In fact, even binary Higgins commutators suffice. As a consequence, in presence of enough...

Semidirect products and split short five lemma in algebraic categories
Speaker: Andrea Montoli (CMUC)
N. Martins Ferreira and M. Sobral proved that, in a pointed regular category C, the split epimorphisms are equivalent to the internal actions if and only if C is protomodular and every internal action is strict. We will show that, even if C is not protomodular, the regular split epimorphisms...

Topological space objects via neighbourhood systems
Speaker: Nelson Martins-Ferreira (IP Leiria/CDRSP)
In this talk we consider the problem of defining a topological space object internal to an arbitrary category (perhaps with some extra structure, or appropriate conditions) in such a way that a topological space object in the category SET, of sets and maps, is a topological space, while, for...

Quantization in complex analysis and operator theory
Speaker: Nelson Faustino (CMUC)
In this talk it will be explored the relevance of quantization on the construction of polyanalytic function spaces likewise its relevance on the study of class of Toeplitz operators obtained from Berezin quantization. Starting from a group representation for the Heisenberg group...

Ribbon Schur functions with full support and Schur positivity
Speaker: Olga Azenhas (CMUC/Univ. Coimbra)
It is known that the Schur expansion of a skew Schur function runs in a subposet of the dominance lattice with top element and bottom element. The support of a skew Schur function consists of the partitions indexing Schur functions which appear in the Schur expansion with a positive...

Tunnel number degeneration under the connected sum of prime knots
Speaker: João Nogueira (CMUC/Univ. Coimbra)
In this talk, a study on 2-string free tangle decompositions of knots with tunnel number two will be presented. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't...

Geometry and Topology of 3-cosymplectic manifolds
Speaker: Antonio de Nicola (CMUC)
In this talk, we deal with 3-cosymplectic manifolds which are the closest odd-dimensional analogue of hyper-Kähler structures, just as cosymplectic manifolds are the closest odd-dimensional analogue of Kähler structures. After a brief introduction to the geometric properties of...

On the solution set of the matrix equation AX-XA=I
Speaker: Eduardo Marques de Sá (CMUC)
Matrix equations like AX-YB=C and AX-XB=C have been extensively studied in the literature because of their importance in linear control. The case AX-XA=I has also been considered, though briefly; as the commutator AX-XA has zero trace, our equation has solutions only if the base field has...

Models and algorithms for network design problems
Speaker: Michael Poss (Univ. Libre de Bruxelles, Belgium)
In this talk, we will have a rapid look at diverse problems arising in the context of network design. We start with a brief introduction to enumeration techniques used in integer programming. Then, we present different problems occurring in telecommunications and electrical power systems. We...

The minimum description length in line transect sampling
Russell Alpizar-Jara (Univ. Évora)
Population density estimation in line transect sampling requires fitting a probability density function denoted by f(y|Ѳ), where y represents the perpendicular distance from a detected animal (or object) to a transect line, and Ѳ represents the vector parameter indexing this...

Global dissipative solutions of a coupled problem for image restoration

Dmitry Vorotnikov (CMUC)


We consider a coupled nonlinear PDE model for image restoration. Both image and edge variables are incorporated by coupling them into two different PDEs. The features of our problem which oppose strong and classical weak well-posedness are the presence of a nonlinear function (modulus) of...

Well-founded and well-pointed coalgebras
Speaker: Lurdes Sousa (IP Viseu/CMUC)
A coalgebra (A,a) of an endofunctor H is well-founded if the square Hm.a'=a.m is not a pullback for any proper subcoalgebra m:(A',a')-->(A,A). For a graph, seen as a coalgebra of the power-set functor, this is exactly the usual definition of well-founded graph, as observed by G. Osius...

Counting dominant regions in the m-extended Catalan arrangement with a fixed separating wall
Speaker: Eleni Tzanaki (Univ. of Crete, Greece)
Athanasiadis introduced separating walls for a region in the m-extended Catalan arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the m-extended Catalan arrangement for type A and calculate the number of dominant regions which have the fixed...

Geometry of Maurer-Cartan elements on complex manifolds
Speaker: Ping Xu (Penn State Univ., USA)

Compactifications of reductive groups as moduli stacks of bundles
Speaker: Johan Martens (Aarhus Univ., Denmark)
We will introduce a class of moduli problems for any reductive group G, whose moduli stacks provide us with (toroidal) equivariant compactifications of G. Morally speaking, the objects in the moduli problem could be thought of as stable maps of a twice-punctured sphere into the classifying...

Anomalous diffusion imaging through fractional order calculus
Speaker: Ercília Sousa (CMUC/Mat. FCTUC)

Applications of retinal imaging with photoreceptor resolution
Speaker: Sérgio Nascimento (Univ. Minho, Braga)

Integer-valued bilinear time series models
Speaker: Isabel Pereira (Univ. Aveiro)
The analysis of count processes has become an important area of research in the last two decades. In this paper we consider the simple non-negative integer-valued bilinear process INBL(1,0,1,1). The parameter estimation is addressed and the problem of forecasting integer-valued time...

Characteristic free resolutions in Schur algebras
Speaker: Ana Paula Santana (CMUC/Mat. FCTUC)
Using the Borel-Schur algebra, I construct explicit resolutions of Weyl modules for GL_n and of co-Specht modules. These resolutions provide an answer to the problem, posed in the 80's by A.Akin and D. A. Buchsbaum, of constructing finite explicit and universal resolutions of Weyl modules by...

A Selection of Insertion-type results Extending Katetov's procedure
Speaker: Javier Gutiérrez García (UPV, Bilbao, Spain)

Normality vs. extremal disconnectedness: two sandwich-type results for the price of one
Speaker: Jorge Picado (Mat.FCTUC/CMUC)
Several results in the literature about normal and extremally disconnected spaces (like Katetov-Tong type theorems, Uryshon's type lemmas or Tietze's type lemmas) shape the idea that the two notions are somehow dual to each other and therefore can be studied in parallel.In this talk we will...

New approaches to rational curves on general hypersurfaces
Speaker: Ethan Cotterill (CMUC)
Almost thirty years ago, Herb Clemens made a series of conjectures about rational curves on general projective hypersurfaces, the most famous of which predicts that every rational curve on a general quintic threefold is rigid, in the sense of deformation theory. In this talk we will discuss...

Betti bounds for the Stanley-Reisner ring of a stellar subdivision
Speaker: Stavros Papadakis (CAMGSD, Lisboa)
The talk will be about recent joint work with Janko Boehm (Saarbruecken) which uses unprojection theory to give bounds for the betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex. ...

Enumeration of Shi regions with a fixed separating wall
Speaker: Ricardo Mamede (CMUC/Mat. FCTUC)
In 2005 Athanasiadis generalized the Narayana numbers by introducing the concept of separating wall for a region in the extended Shi arrangement. Using this concept, Susanna Fishel, Eleni Tzanaki and Monica Vazirani were able to calculate the number of dominant regions which have a fixed...

Geometric Invariant Theory for polarized curves
Speaker: Margarida Melo (CMUC/Mat FCTUC)
Geometric Invariant Theory (GIT) was introduced by Mumford and co-authors in order to deal with the problem of constructing quotients of algebraic varieties by the action of an algebraic group. It is particularly useful in the construction of moduli spaces within the category of algebraic...

Non-smooth analysis and optimization
Speaker: Suvendu Ranjan Pattanaik (DMUC)
In this talk, we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the so-called approximate multiplier rule and we prescribed an approximate gradient multiplier rule in handling non-smooth problems. Also in this talk we will cover some of...

Tropical Teichmuller theory
Speaker: Filippo Viviani (CMUC/Roma Tre)
I will report on a joint work in progress with M. Chan and M. Melo in which we study a tropical analogous of the classical Teichmuller theory. In particular, we prove that the moduli space of pure tropical curves (constructed in a joint work with S. Brannetti and M. Melo) is the quotient of...

Positivity, sums of squares and real algebraic varieties
Speaker: João Gouveia (Mat FCTUC)
In recent years, the theory of sums of squares emerged as a very useful tool for polynomial optimization. The development of approximation methods based on classic Positivstellensatzes, raised a number of interesting theoretical questions that relate to very classic subjects of algebraic...

Lifts of convex sets
Speaker: João Gouveia (Mat FCTUC)
It is well-known that some complicated polytopes can be represented as projections of much simpler polytopes permitting polynomial time algorithms for linear optimization over them. In 1991 Yannakakism established a connection between the existence of such lifts and the nonnegative rank of...

Moment analysis of distributions: classical and recent results
Speaker: Jordan Stoyanov (Newcastle Univ., UK)
The main discussion will be on distributions and their characterization in terms of the moments. There are distributions which are unique (M-determinate) and others which are non-unique (M-indeterminate). When analyzing specific stochastic model we clarify why in some cases a distribution...

Dualities in modal logics via the Kleisli construction
Speaker: Dirk Hofmann (U. Aveiro)
Motivated by questions in semantics of modal (propositional) logics, over the past years several duality results were established which extend the classical Priestley and Stone dualities. In this talk we will show how the Kleisli construction for monads can simplify their proof and...

Estimating the adjustment coefficient in Risk Theory
Speaker: Ana Cristina Moreira de Freitas (Fac. Economia, Univ. Porto)
We consider the problem of estimating the adjustment coefficient R in the Sparre Andersen model, which allows us to estimate upper bounds for the ruin probability of insurance companies.We propose a consistent estimator for R and establish a result about its asymptotic normality. Moreover,...

Sets with small sumset and small periodic product-set
Speaker: Cristina Caldeira (CMUC/Mat. FCTUC)
We characterize the pairs (A,B) of finite non-empty subsets of a field such that the product-set, AB, is periodic and both the sumset, A+B, and the product-set, AB, are as small as possible, that is, |A+B|=min{p, |A|+|B|-1} and |AB|=max{|A|,|B|}, where p is the characteristic of the...

Veering triangulations admit strict angle structures
Speaker: Henry Segerman (University of Melbourne, Australia)
Agol recently introduced the concept of a veering taut triangulation of a 3-manifold, which is a taut ideal triangulation with some extra combinatorial structure. Hodgson, Rubinstein, Tillmann and I show that each veering triangulation admits a strict angle structure, which is a necessary...

The subgroup restriction problem for the general linear group
Speaker: Emmanuel Briand (Univ. Sevilla, Spain)
Let H ⊂ G be reductive groups. Each irreducible representation of G is also a representation of H, but not necessarily irreducible. How does it decompose into irreducibles ? How to describe and compute the multiplicities in its decomposition ? This is the "subgroup restriction...

Baire sets and the Boolean reflection of sigma-frames
Speaker: Bernhard Banaschewski (McMaster University, Canada)
For any topological space X, the σ-field BX of its Baire sets is the Boolean sub-σ-algebra of the power set of X generated by the σ-frame Coz X of the cozero sets of X. Apart from this, one obviously has the abstractly defined Boolean σ-frame reflection BCoz X and the...

On monotone normality and subfitness
Speaker: Javier Gutiérrez García (Univ. Basque Country, Bilbao, Spain)
The notion of monotone normality was introduced in 1973 by Heath, Lutzer and Zenor as a strengthening of normality and is probably what you would guess if asked to define "normal in a monotone way". Every metrizable space and every linearly ordered space is monotonically normal. In...

Nonmeasurable cardinals and pointfree topology
Speaker: Bernhard Banaschewski (McMaster University, Canada)
The familiar classical results that(i) any extremally disconnected P-space of nonmeasurable cardinal is discrete, and(ii) any discrete space of nonmeasurable cardinal is realcompactare shown to be consequences of much more general results concerning frames. The particular frames involved...

Injectivity and the fibrewise way-below relation
Speaker: Maria Manuel Clementino (Mat.FCTUC/CMUC)
Using results of Escardó-Flagg [1] and Hofmann [2], we characterize continuous maps which are injective with respect to special classes of embeddings. These characterizations are based on a fibrewise way-below relation which generalizes the one used by Richter in his characterization...

The weighted Stieltjes inequality and application

Amiran Gogatishvili (Institute of Mathematics of the Czech Academy of Sciences, Czech Republic)

Let $1<p\leq q<\infty$. Inspired by some results concerning characterization of weighted  Hardy type inequalities, where the equivalence of four scales of integral conditions was proved, we use related ideas to find some new equivalent scales of integral conditions related to the...

The degree and the half degree principle for symmetric polynomials
Speaker: Alexander Kovacec (Mat. FCTUC)
Vlad Timofte proved in 2001/2 that a symmetric real polynomial F of degree d in n variables is nonnegative on certain subsets of Rn if and only if it is so on the subset of points with at most max{|_d/2_|,2} distinct components. His proof used ordinary differential equations. Quite...

Projecções empíricas e cartas antigas
Speaker: Joaquim Alves Gaspar (Centro Interuniversitário de História das Ciências e da Tecnologia, FCUL)
O conceito de "projecção empírica" foi utilizado em 1977, pelo geógrafo americano Waldo Tobler, para designar as representações cartográficas construídas de modo a obter determinadas propriedades, através de...

A glimpse on vector invariant theory I. The characteristic zero approach (after Capelli and Weyl)
Speaker: Francesco Regonati (Università di Bologna)
The characteristic zero approach can be founded on the so-called Weyl's Theorem (H. Weyl, The Classical Groups, 1946) which essentially says that a system of generators for the algebra of (absolute) vector invariants for any subgroup G of GL(d) can be constructed by polarizing a system of...

A glimpse on vector invariant theory II. The characteristic free approach (after Rota and De Concini and Procesi)
Speaker: Andrea Brini (Università di Bologna)
The structure of this talk is the following: -The starting point is the straightening formula for bideterminants (Doubilet, Rota, Stein, 1974) and its analogs for Pfaffians and Gramians (De Concini, Procesi 1976). - From the straightening formulae one derives versions of the E. Pascal...

Multi-criterion optimization of a public transport network
Speaker: Carlos Caçador (Novabase)
The shortest path problem is a well-known and widely studied problem of operational research. Although used in several areas, is in the area of...

The singular fibre of the Hitchin map
Speaker: Peter Gothen (Mat. FCUP / CMUP)
A Hitchin pair on a complex projective curve consists of a vector bundle and an endomorphism of this bundle, twisted by a fixed line bundle L. Thus, when L is the canonical bundle of the curve, a Hitchin pair is a Higgs bundle. There is a Hitchin map from the moduli space of Hitchin pairs to...

Two problems combining routing and location
Speaker: Marta Pascoal (DMUC)
In this talk we describe two problems that combine the determination of a route between two given nodes in a network and the location of a set of special nodes along the route, the minimum cost path problem with relays and the pipeline and valve location problem. It is shown that rather than...

Curves on irregular surfaces
Speaker: Margarida Mendes Lopes (CAMGSD / IST)
The existence of global 1-forms on surfaces of general type imposes constraints on the existence of curves of low genus on the surface. Also sometimes the existence of certain curves on these surfaces allows us to understand or characterize the surface. In this talk I'll discuss some of...

Support vector machines in medical image analysis
Speaker: Rui Bernardes, Pedro Serranho, João Duarte (IBILI, Coimbra)
Support Vector Machines (SVM) are a classification tool with broad applications. The process is based on the representation of each element of the set in a multidimensional feature space.This machine learning method relies then on optimization to find a set of splitting hyperplanes that...

In vitro drug dissolution profiles: comparison and mathematical modeling
Speaker: Carla M. Lopes (Univ. Fernando Pessoa)

Evaluating the Fréchet derivative of the matrix pth root
Speaker: João Cardoso (ISEC)
It is well-known that the sensitivity of the matrix pth root (and primary matrix functions in general) to small perturbations in the data is measured by a condition number based on the norm of the Fréchet derivative. In this talk we show that computing the Fréchet derivative of...

On the birational geometry of the universal Picard variety
Speaker: Filippo Viviani (CMUC/Univ. Roma 3)
We compute the Kodaira dimension of the universal Picard variety parameterizing line bundles of degree d on curves of genus g under the (technical) assumption that gcd(d-g+1,2g-2)=1. We also give partial results for arbitrary degrees d and we investigate for which degrees the universal...

Hyperplane arrangements: bijections and enumeration
Speaker: Alessandro Conflitti (CMUC)
We survey some recent combinatorial results about bijections between objects connected with hyperplane arrangements, such as dominant regions and alcoves, and other combinatorial objects such as partitions and tableaux, and we present some enumerative formulae. ...

Optimal embeddings of spaces of generalized smoothness in the critical case
Speaker: Cornelia Schneider (University of Erlangen, Nuremberg)

Euclidean, hyperbolic and spherical geometries in the Landau equation with magnetic field
Speaker: Zouhair Mouayn (Sultan Moulay University, Morroco)
We review the definition and properties of coherent states, their fundamental role in quantum mechanics as well as their most known generalizations with examples. We focus on the Gilmore-Perelomov approach in constructing coherent state by means of the representation theory of Lie groups and...

The generating function of simultaneous s/t-cores
Speaker: William Keith (CELC, Lisboa)
Previous work on partitions simultaneously s-core and t-core has enumerated such partitions broadly, but missing from the literature is a description of the generating function that would count them. We can produce one, following part of Jaclyn Anderson's original proof of the overall number...

Scott approach spaces
Speaker: Gonçalo Gutierres (Mat. FCTUC/CMUC)
Approach spaces, introduced by R. Lowen in 1989, constitute a generalization of both topological and metric spaces. There are several ways of describing them, among the most common are the one using distances between points and sets, and the one using numerified convergence which tells how...

Approaching metric domains
Speaker: Dirk Hofmann (U. Aveiro)
In analogy to the situation for continuous lattices which were introduced by Dana Scott as precisely the injective T_0 spaces via the (nowadays called) Scott topology, we study those metric spaces which correspond to injective T_0 approach spaces and characterise them as precisely the...

Problemas de cavidade totalmente não-lineares

Eduardo Teixeira (Universidade Federal do Ceará, Brasil)

Dado um aberto O de Rn e uma função f \ge 0 na fronteira de O, um questionamento fundamental em matemática aplicada refere-se à solução do seguinte problema de fronteira livre: \Delta u = 0 ~ {u> 0\}, \quad u = f ~ \partial O, u_\nu = 1 ~\partial...

Schur positivity and Littlewood-Richardson coefficient inequalities in the multiplicity-free case
Speaker: Olga Azenhas (CMUC/Mat FCTUC)
A symmetric function is said to be Schur positive (or nonnegative) if its expansion in the Schur basis has only nonnegative integer coefficients. In the recent years, several problems concerning the Schur positivity of certain differences of Schur function products of the form s_\rho ...

Equivariant degenerations of spherical modules
Speaker: Stavros Papadakis (CAMGSD, Lisboa)
Given a reductive algebraic group G and an invariant Hilbert function h, Alexeev and Brion have defined a moduli scheme M which parameterizes affine G-schemes X with the property that the coordinate ring of X decomposes, as G-module, according to the function h. The talk will be about joint...

Intersection patterns of convex sets
Speaker: Martin Tancer (Charles Univ., Czech Republic)
Classical Helly's theorem states that if n>d subsets of d-dimensional Euclidean space are such that each d+1 of them have nonempty intersection then the intersection of all is non empty. This theorem can be seen as a theorem on intersection patterns of convex sets. The question of...

The moment problem for continuous positive semidefinite linear functionals
Speaker: Salma Kuhlmann (Universität Konstanz, Germany)
Let V be the countable dimensional real polynomial algebra. Let \tau be a locally convex topology on V. Let K be a closed subset of Rn, and let M := M{g1,..., gs} be a finitely generated quadratic module in V. We investigate the following question:When is the cone Psd(K) (of polynomials...

Linear Matrix Inequality (LMI) representation of convex semialgebraic sets
Speaker: Victor Vinnikov (Ben Gurion University, Israel)
Semidefinite programming (SDP) is a powerful new approach in optimization that has blossomed since the mid 1990s. In a SDP problem, we maximize or minimize a linear functional over a convex set in Rd given by {(x1,...,xd) : A0 + x1 A1 + ... + xd Ad \geq 0}, where A0,A1,...,Ad are real...

The Riemann-Hilbert method and the limit behavior of the reproducing kernels
Speaker: Vitor Sousa (CIDMA, Aveiro)

Semidirect products in Jonsson-Tarski varieties
Speaker: Andrea Montoli (CMUC)
The aim of this talk is to characterize those split extensions corresponding to the classical semidirect product in Jonsson-Tarski varieties, with particular attention to the cases of monoids and unitary magmas, and to compare the classical notion of semidirect product with the categorical...

Internal categorical structures in weakly Mal'tsev categories
Speaker: Nelson Martins-Ferreira (IP Leiria)
It is well known that in the context of a Mal'tsev category the three notions: multiplicative graph, internal category, internal groupoid; coincide and are completely determined by the respective underlying reflexive graph. In this talk we will see that in the more general case of a weakly...

Compactified Jacobians of singular curves
Speaker: Margarida Melo (CMUC/Mat FCTUC)
The Jacobian variety of a smooth curve is an Abelian variety that carries important information about the curve itself. Its properties have been widely studied along the decades, giving rise to a significant amount of beautiful mathematics. However, for singular curves, the situation is more...

Parameterized linear codes and algebraic invariants
Speaker: Maria Vaz Pinto (CAMGSD/IST)
Let K be a finite field and let X be a subset of a projective space over the field K, which is parameterized by the monomials arising from the s edges of a clutter. If S=K[t_1,.., t_s] and I(X) is the vanishing ideal of X, we describe when I(X) is a complete intersection, and in that case we...

Parabolic Kazhdan-Lusztig R-polynomials for tight quotients of the symmetric groups
Speaker: Francesco Brenti (Univ. of Roma "Tor Vergata", Italy)
We study the parabolic Kazhdan-Lusztig R-polynomials for the tight quotients of the symmetric groups. More precisely, we obtain explicit combinatorial product formulas for these polynomials. As an application of our results, we derive combinatorial closed product formulas for certain sums...

A combinatorial approach to assess the separability of clusters
Speaker: Jorge Orestes Cerdeira (Instituto Superior de Agronomia, U. T. Lisboa)
Separability of clusters is an issue that arises in many different areas, and is often used in a rather vague and subjective manner. We introduce a combinatorial notion of interiority to derive a global view on separability of a set of entities. We develop this approach further to evaluate...

A categorical invariant of flow equivalence
Speaker: Alfredo Costa (Mat. FCTUC/CMUC)
The Karoubi envelope of a semigroup is a small category which plays a distinguished role in finite semigroup theory thanks to the Delay theorem of Tilson. In this talk, an application to the classification of symbolic dynamical systems is presented: up to natural equivalence, the Karoubi...

A mapping space for Gray-categories
Speaker: Björn Gohla (U. Porto)
It is well known that connections on a principal G-bundle over a manifold M can be represented by group homomorphisms LM-->G, where LM is the loop group of M. Similarly, 2-connections can be seen as 2-functors from a 2-groupoid of points, paths and bigons in M to a 2-group G.In passing to...

Twisted multi-derivations
Speaker: Christian Lomp (CMUP/Mat. FCUP)
A differential graded algebra on a non-commutative algebra A is interpreted as the space of differential forms on A and is usually referred to as a differential calculus on A. Connections in non-commutative geometry are maps from a module M to M tensored with the space of one-forms that...

Admissible sign patterns for certain classes of matrices
Speaker: Cláudia Mendes Araújo (Dep. Matemática, Univ. Minho)
In qualitative and combinatorial matrix theory, a methodology based on the use of combinatorial information such as the signs of the elements of a matrix is very often useful in the study of some properties of matrices. A matrix whose entries are chosen from the set {+,-,0} is called a sign...

Direct search methods: robustness and efficiency in derivative-free optimization
Speaker: Ana Luísa Custódio
In this talk we will focus on the numerical optimization of extended-value, nonsmooth functions, without using derivatives. We will start by reviewing the class of directional Direct Search Methods, paying particular attention to the situation where the objective function is...

Numerical schemes for short wave long wave interaction equations
Speaker: Paulo Amorim (CMAF/Univ. Lisboa)
We prove convergence of some finite volume type numerical schemes for short wave long wave interaction equations. These are systems of coupled nonlinear PDEs consisting of a Schroedinger equation for the short waves and a hyperbolic conservation law modeling the long waves. We present some...

The Calabi-Yau equation for Lagrangian fibrations
Speaker: Luigi Vezzoni (Università di Torino, Italy)
The Calabi-Yau equation on Almost-Kaehler manifolds is an elliptic equation arising from a natural generalization of the Calabi conjecture to the non-complex context. This equation was introduced by Donaldson who proved that its solutions are unique and Tosatti, Weinkove and Yau proved that...

On the number of finite algebras
Speaker: Peter Mayr (CAUL)
In 1941 Emil Post showed that there are only countably many, essentially distinct algebraic structures of size 2. Here we consider two algebras as essentially the same (term equivalent) if they have the same term functions. As an example of term equivalent structures we may consider a...

Semidirect products of internal groupoids
Speaker: Andrea Montoli (CMUC)
We give a characterization of those finitely complete categories with initial object and pushouts of split monomorphisms that admit categorical semidirect products. As an application we examine the case of groupoids with fixed set of objects. Further, we extend this to the internal...

A classical umbral view of the Riordan group and related Sheffer sequences
Speaker: José Agapito Ruiz (CELC)
The Riordan group is the set of infinite lower triangular invertible matrices with the group operation given by a matrix multiplication that combines both the usual Cauchy product and the composition of formal power series. It is related to a broad family of polynomial sequences in one...

The Gyrangle
Speaker: George Hart (The Museum of Mathematics, New York, USA)
George Hart will present a novel geometric structure that produces a gyroid surface entirely from equilateral triangles. This construction is the basis of a 1m diameter sculpture constructed from hundreds of laser-cut steel units, bolted together by hundreds of members of the public at a...

Well-posedness of dynamics of microstructure in solids

Yasemin Sengul (CMUC)

This talk will be on the problem of well-posedness of nonlinear viscoelasticity under the assumptions allowing for phase transformations in solids. In one space dimension existence and uniqueness of the solutions for the quasistatic version of the model is proved by means of approximating...

Sub-semi-Riemannian geometry on Heisenberg-type groups

Anna Korolko (University of Bergen, Norway)

Sub-semi-Riemannian geometry is a new subject generalizing sub-Riemannian and semi-Riemannian geometries. I will introduce basic notions and facts from the theory of sub-semi-Riemannian geometry, show examples of sub-semi-Riemannian manifolds, namely, some Heisenberg-type...

A class of rigid representations associated to linear PDE
Speaker: Pedro C. Silva (Instituto Superior de Agronomia, U. T. Lisboa)
The monodromy of the local holomorphic solutions of Gauss's hypergeometric equation defines a linear representation of the fundamental group of the Riemann sphere with 3 points removed. This monodromy is therefore determined by matrices A,B,C verifying the relation ABC=I. Riemann...

Distributive law between a monad and a comonad
Speaker: Ivan Yudin (CMUC)
This work is mainly motivated by the modern approach to the deformation theory of associative algebras.The idea is to unify notions of different <i>\infty</i>-algebras, such as <I>A<sub>\infty</sub></i>-algebras or...

A "one for the price of zero" duality principle for distributive spaces
Speaker: Dirk Hofmann (U. Aveiro)
Our study of topological spaces presented as convergence structures shaped the ideathat "topological spaces are generalised orders", and eventually revealed thefollowing analogies. down-closed...

Schwarz waveform relaxation algorithms for some semilinear reaction-advection-diffusion type equations
Speaker: Filipa Caetano (Univ. Paris-Sud 11, France)
We are interested in domain decomposition algorithms of Schwarz waveform relaxation type to compute approximate solutions of some nonlinear evolution equations. Schwarz waveform relaxation algorithms are based on a decomposition of the problem in space, like classical Schwarz methods,...

Mathematics Training and Talent Search Programme
Speaker: Ajit Kumar (Dep. Math., Inst. of Chemical Technology, Mumbai, India)
Mathematics Training and Talent Search Programme (M.T. & T.S.) is a national levelfour weeks intensive summer training programme in mathematics which has been runningsince 1993 in India. This programme is funded by the National Board for Higher Mathe-matics (NBHM) and is directed by S....

Exploration of genomewide data: future challenges and the state of the art
Speaker: Magnus Fontes (Lund University, Sweden)
I will present a collection of statistical and mathematical methods useful for the exploration of some types of multivariate data and in practice show how we have implemented them in the commercial software Qlucore Omics Explorer (QOE). In particular I will discuss classical principal...

High and massive excursions of Gaussian processes

Juerg Husler (Univ. Bern, Switzerland)


On cographic toric face rings
Speaker: Filippo Viviani (CMUC/Roma Tre)
Toric face rings were introduced by Stanley as a simultaneous generalization of simplicial face rings and toric rings. In this talk, I will report on a joint work in progress with S. Casalaina-Martin and J. L. Kass, in which we study certain toric face rings associated to graphs. The...

Legendre foliations on contact manifolds and related topics

Beniamino Cappelletti Montano (research visitor at CMUC)

In this talk some recent results on the theory of Legendre foliations on contact Riemannian manifolds will be reviewed. In particular, we will discuss about Legendre foliations on Sasakian manifolds, bi-Legendrian structures and contact metric (\kappa,\mu)-spaces. Such results will be...

The proposal of a bone remodeling model based on generalized thermodynamics potentials
Speaker: Emílio Graciliano Ferreira Mercuri (Univ. Porto / Univ. Fed. Paraná, Brasil)
The bones are the elements responsible to support the body and one of their main characteristics is the capability of self adaptation, which consists in continuous changes in their microstructure during life-time. The process responsible for this modification is called internal remodeling...

On the deformations of N-Koszul algebras
Speaker: Mariano Suarez-Alvarez (Universidad de Buenos Aires, Argentina)
There are two natural notions of deformation applicable to N-Koszul algebras.First, such an algebra can be presented by generators and relations using homogeneous relators of degree N, and it is natural to consider those algebras which are obtained by changing the relators by adding to them...

Graduações das álgebras de Lie simples
Speaker: Alberto Elduque (Departamento de Matemáticas, Universidade de Saragoça, Espanha)
As graduações para as álgebras de Lie clássicas foram descritas recentemente incluindo o caso modular. Neste conferência apresentam-se as técnicas utilizadas e comentam-se os últimos trabalhos sobre as álgebras de Lie excepcionais. ...

Twisted contact groupoids and integration of twisted Jacobi structures
Speaker: Fani Petalidou (Aristotle University of Thessaloniki, Grécia)

Resolutions, higher extensions and the relative Mal'tsev axiom
Speaker: Tim Van der Linden (CMUC)
We study how the concept of higher-dimensional extension which comes from categorical Galois theory relates to simplicial resolutions and homology. For instance, an augmented simplicial object is a resolution if and only if its truncation in every dimension gives a higher extension, in which...

A Schreier-Mac Lane extension theorem in action accessible categories
Speaker: Andrea Montoli (CMUC)
The aim of this talk is to give an intrinsic version of the Schreier-Mac Lane extension theorem, classically known for groups: on the set Ext(Y,K) of isomorphism classes of extensions with fixed abstract kernel there is a simply transitive action of the abelian group Ext(Y,ZK), where ZK is...

Internal categories in n-permutable varieties
Speaker: Diana Rodelo (U. Algarve/CMUC)
We show that the notions of internal category and internal groupoid coincide for any n-permutable variety....

A module model for Azenhas' bijection
Speaker: Itaru Terada (Grad. School of Math. Sci. Univ. of Tokyo, Japan)
In the spirit of Steinberg's description of the Robinson-Schensted correspondence, or van Leeuwen's description of the Schützenberger involution, we give an interpretation of Azenhas' bijection on Littewood-Richardson tableaux as a bijection between the irreducible components of an...

Daniell's version of Lebesgue integral II
Speaker: Ales Pultr (Charles Univ., Prague, Czech Republic)
This is the second and last lecture of a short course on the integral introduced and developped by Percy John Daniell in his article "A general form of integral", Annals of Mathematics 19 (1918) 279-294.The course will consist on two lectures, 1h30m each.Lecture notes of the course...

Fibrewise injectivity and Kock-Zoberlein monads
Speaker: Maria Manuel Clementino (Mat. FCTUC/CMUC)
In this talk we will apply the Theorem of Escardó-Flagg [2] characterizing injective objects as algebras for a Kock-Zoberlein monad to the characterization of injective morphisms, making use of a lifting of a Kock-Zoberlein monad to the corresponding slice categories. This result...

Numerical methods that preserve the fixed points of a differential equation
Speaker: Higinio Ramos (Departamento de Matemática Aplicada, Univ. Salamanca, Espanha)

Daniell's version of Lebesgue integral I
Speaker: Ales Pultr (Charles Univ., Prague, Czech Republic)
This is the first lecture of a short course on the integral introduced and developped by Percy John Daniell in his article "A general form of integral", Annals of Mathematics 19 (1918) 279-294.The course will consist on two lectures, 1h30m each.Lecture notes of the course may be...

Landau's necessary conditions for the Hankel transform
Speaker: Afonso Bandeira (DMUC)
We will prove Landau-type necessary density conditions for sampling and interpolation on spaces of functions whose Hankel transform is supported in a measurable subset $S$ of the positive semi-axis, in particular we prove the existence of an optimal Nyquist rate. As a special case, necessary...

Jacobi structures in supergeometric formalism
Speaker: Paulo Antunes (FCTUC/CMUC)
In this talk, we state and prove most known results (established by Iglesias-Marrero and Grabowski-Marmo) about Jacobi algebroids and bialgebroids using the supergeometric formalism, more precisely, the so-called "big bracket", a formalism where brackets and anchors are encoded by...

Quasilinear singular equations
Speaker: Tommaso Leonori (University of Granada, Spain)

Upper bounds for the energy of digraphs
Speaker: Elias Rojas (PhD programme U. Coimbra/U. Porto)
Let D be a digraph, its energy is defined as the sum of the absolutes values of the real parts of the eigenvalues of its adjacency matrix A(D). This concept was introduced by J. Rada in 2008 as a generalization of the concept of graph energy introduced by I. Gutman in 1978. The concept of...

Ergodic transitions in continuous-time random walks
Speaker: Roberto Venegeroles (Centro de Matemática, Computação e Cognição - UFABC - Brazil)
Abstract: We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general  expression for the distribution of time-averaged observables for such systems, generalizing some recent results presented in the literature. For...

Regularized models for strongly nonlinear internal solitary waves
Speaker: Ricardo Barros (BCAM, Bilbao, Spain)
We consider strongly nonlinear long wave models for large amplitude internal waves in two-layer flows. Both rigid-lid and free-surface are set for the upper boundary. It is shown that these models suffer from Kelvin-Helmholtz (KH) instability so that any given shear (even if arbitrarily...

Generalized down-up algebras: their symmetries and arithmetic
Speaker: Samuel Lopes (CMUP/Mat. Pura FCUP)
Generalized down-up algebras were introduced by Cassidy and Shelton (J Alg 2004) as a generalization of down-up algebras, originally defined by Benkart and Roby (J Alg 1998). The latter were motivated by combinatorial operators on a (q, r)-differential poset.Those generalized down-up...

Poly-Bergman spaces on domains Möbius equivalent to a disk
Speaker: Luis V. Pessoa (IST, Lisbon)
Let $U$ be a complex domain Möbius equivalent to a disk and let $j$ be a non zero integer. The talk will focus on explicit representation of the poly-Bergman projection of order $j$ in terms of the canonical two-dimensional singular integral operators. One also shows how the Lebesgue...

Compact generation for Lie groupoids
Speaker: Nicolas Raimbaud (Université de Nantes)
In the 80's, André Haefliger introduced the problem of compact realization for foliations -- which is still open, and gave a sufficient condition for realization, the compact generation of the holonomy pseudogroup. We introduce a Morita-invariant notion of compact generation for...

Limits of inhomogeneous problems related to the p(x)-Laplacian
Speaker: Mayte Perez-Llanos (IST, Lisbon)

Highly accurate computation of eigenvalues of tridiagonal matrices
Speaker: Rui Ralha (U. Minho)
We present a method to improve or just guarantee the accuracy of the approximations delivered by any fast method for the eigenvalues of symmetric tridiagonal matrices.The motivation for this approach is two-folded: 1) the fastest state-of-the-art routines in LAPACK do not always deliver...

Estimação adaptativa e invariante do índice de valores extremos
Speaker: Maria Ivette Gomes (Univ. Lisboa)
Iremos abordar um método de estimação semi-paramétrica de viés-reduzido de um índice de valores extremos (EVI, do Inglês, extreme value index) positivo. Neste contexto de caudas-direitas pesadas, os estimadores clássicos do EVI...

The voice transform of the Blascke group generated by a representation on the weighted Bergman spaces
Speaker: Margit Pap (Univ. Pécs, Hungary)
In this talk are presented results connected to the voice transform of the Blaschke group generated a representation of the group on the weighted Bergman spaces {\cal{H}}^m(\Bbb D). We give a representation U_a of Blaschke group on the weighted Bergman spaces {\cal{H}}^m(\Bbb D), we compute...

Mesoscale cracking of composites

Miguel Patrício (CMUC and Instituto Politécnico de Leiria)

The usage of composites in high performance products such as aerospace components, storage tanks or racing car bodies is increasing. Typically, a lightweight yet strong material is sought, capable of withstanding harsh loading conditions. Such conditions are prone to the occurrence of...

On the full interval linear expansion of a skew-Schur function
Speaker: Ricardo Mamede (CMUC/Mat. FCTUC)
A skew-Schur function can be expressed as a sum of Schur functions with non-negative integer multiplicities given by the well-known Littlewood-Richardson coefficients. These coefficients also govern the decomposition of a product of two Schur functions as a sum of Schur functions....

Connected subgraphs in multicoloured graphs
Speaker: Henry Liu (FCT-CMA/FCTUNL)
In graph theory, a well-known observation of Erdős and Rado which is often considered as folklore; in fact it is also the first exercise in Béla Bollobás' book "Modern Graph Theory", is the following: For any graph, either it is connected, or its complement...

Quantum integrability and combinatorics: alternating sign matrices, plane partitions and completely packed loops
Speaker: Tiago Dinis (Université Pierre et Marie Curie)
1, 2, 7, 42, 429, 7436...This sequence appeared for the first time in the study of Alternating Sign Matrices at the beginning of the 80'. With time, mathematicians and physicists got used to seeing this mysterious sequence appear counting sets apparently so different.In this talk I will...

Supercharacter theories, root systems and set partitions
Speaker: Carlos André (CELC/Mat. FCUL)
In this talk, we survey the basics of supercharacter theories of finite groups with particular emphasis on the finite classical groups of Lie type. We will discuss some (mysterious) connections with the combinatorics of the underlying root system, and show how some supercharacter-theoretic...

Maximal subgroups of free profinite semigroups
Speaker: Alfredo Costa (Mat.FCTUC/CMUC)
Free profinite semigroups proved to be a fundamental tool for the development of Finite Semigroup Theory since the mid 1980's. However, little is known about their structure. The first important advances were made in the last decade, based in a beautiful connection with symbolic dynamics...

Bernstein estimates for systems of weakly coupled fully non-linear elliptic equations and integral operators
Speaker: Gabrielle Terrone (IST, Lisbon)
Bernstein estimates permit to bound the sup-norm of the gradient of the solution with the sup-norm of the solution. We are particularly interested in systems that arise in the stochastic optimal control problems of hybrid systems, that are systems of weakly coupled nonlinear elliptic...

Non convex Aubry-Mather measures
Speaker: Filippo Cagnetti (IST, Lisbon)
Given a smooth Hamiltonian H, we study the existence of measures invariant under the Hamiltonian flow, when H is non-convex. To simplify the treatment, we restrict ourselves to the periodic setting. Due to the lack of convexity, it is not possible to pass to the Lagrangian formulation, and...

Noncrossing and nonnesting partitions of classical Weyl groups
Speaker: Alessandro Conflitti (CMUC)
We study noncrossing and nonnesting partitions of classical Weyl groups, and we describe bijections preserving openers, closers and transients, between these two kinds of combinatorial structures, with some special emphasis on Coxeter systems of type $D$. This is a joint project with Ricardo...

On the detection of an immersed rigid body

Ana Leonor Silvestre (IST, Lisboa)


Stability and moduli spaces of syzygy bundles
Speaker: Pedro Macias Marques (U. Évora)
It is a longstanding problem in Algebraic Geometry to determine whether the syzygy bundle E_{d_1,...,d_n} on P^N defined as the kernel of a general epimorphism  \phi: O(-d_1)\oplus\cdots\oplus O(-d_n) -> O is (semi)stable. In this talk, attention is restricted to the case of...

Numerical methods for Volterra integral equations with weakly singular kernel
Speaker: Teresa Diogo (CEMAT/Instituto Superior Técnico, Lisboa)
This talk is concerned with the numerical solution of a Volterra integral equation with non-standard weakly singular kernel which may arise in connection with some heat transfer problems. The singular behaviour of the solution near the origin causes the loss of the optimal (global)...

Motives toward a pointfree study of completions of functorial (quasi)-uniformities on frames/locales
Speaker: Guillaume Brummer (University of Cape Town, South Africa)

Local well-posedness for generalized KP-II type equations on cylinders
Speaker: Jorge Drumond Silva (IST, Lisboa)
We present recent results for the KP-II equations with generalized dispersion terms, in two and three spacial dimensions, periodic only in the x variable. We will start by showing how the solutions to the linearized equations satisfy bilinear Strichartz-type estimates, which are independent...

Realizing modules over the homology of a DGA
Speaker: Gustavo Granja (CAMGSD/IST)
Let A be a DGA over a field. A graded module X over H_*(A) is said to be realizable if there exists a DG module M over A with H_*(M)\cong X. There are at least two approaches to finding out whether a module is realizable. One uses Postnikov systems (certain diagrams in the derived category...

A homological hammer to pound an infinite problem into a finite calculation
Speaker: Thomas Cassidy (Bucknell University, USA)
A list of generators and relations offers a succinct presentation for an algebra over a field, but what can we deduce when looking at this presentation? If two algebras have similar presentations, they may also share other characteristics. I will illustrate several ways in which...

Frobenius manifolds and dispersionless integrable hierarchies
Speaker: Guido Carlet (CMUC)
We review the construction of the principal hierarchy associated to a Frobenius manifold....

Partial colorings, posets and chromatic polynomials
Speaker: Domingos Cardoso (U. Aveiro)
Each partial coloring of a vertex subset W of a graph of order n defines a poset whose elements are minors. These minors are obtained by the contraction of edges such that the end-vertices have the same color from an arbitrary vertex coloring of the complement of W. In each of these posets,...

Mixed-type functional differential equations: analysis and computational methods
Speaker: Pedro Lima (Instituto Superior Técnico, UTL)
Abstract in attachment ...

Hook partitions and coding theory
Speaker: Maria Manuel Torres (CELC/Mat. FCUL)
I will speak about a curious connection between multilinear algebra and coding theory, which was obtained while studying the structure of critical orbital sets associated to hook partitions - this is a joint work with Pedro Cristiano Silva (ISA-UTL)....

Normalities and commutators
Speaker: Sandra Mantovani (Universitá di Milano, Italy)
We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of this commutator. Our main result is to extend to any...

Duality Groups
Speaker: Daniel Pinto (CMUC/Mat.FCTUC)

Folding up of monotone and concordant morphisms for sub-reflections from models in the category of presheaves
Speaker: João Xarez (Universidade de Aveiro)
It will be presented a simplified version of the sufficient conditions for the concordant-dissonant and monotone-light factorizations to coincide, in the case of an adjunction from the category of presheaves on sets into a cocomplete category, satisfying the faithfulness of the composite of...

Jets of foliations
Speaker: Eduardo Esteves (IMPA-Brasil)
We will show how to associate sheaves of jets to singular foliations of algebraic varieties, and discuss some of their applications....

Projectively normal embeddings of curves with general moduli
Speaker: Claudio Fontanari (Università Degli Studi Di Trento, Italy)
In this talk I am going to present a joint work with Edoardo Ballico motivated by a stimulating conjecture due to Aprodu and Farkas. Our main contribution is a suitable improvement in the case of general curves of the classical theorem by Green and Lazarsfeld on the projective normality of...

Compatibilities and Lie algebroid structures. Examples in hyperkähler structures
Speaker: Paulo Antunes (Dep. Mat. FCTUC/CMUC)

Inverse scattering problems and medical imaging
Speaker: Pedro Serranho (IBILI, Coimbra)
Inverse Scattering Problems have a wide range of applications, as radar  and sonar, seismology and medical imaging. In this talk we intend to  present a brief discussion on some particular inverse scattering  problems, focusing on their mathematical formulation and...

Lie algebroids and related structures in supergeometric terms

Paulo Antunes (Dep. Mat. FCTUC/CMUC)


The ratio field of values, properties and related objects
Speaker: Charles R. Johnson (College of William and Mary, USA)
A variation on the classical field of values recently arose in numerical analysis. Instead of one matrix, it is a function of two, in which each set element is a ratio of Hermitian quadratic forms at the same vector, as the vectors run over the unit sphere. In the denominator is a matrix...

Action-angle variables : the Poisson case, around a singular leaf
Speaker: Camille Laurent-Gengoux (CMUC)

Unprojection and Stanley--Reisner rings associated to cyclic polytopes
Speaker: Stavros Papadakis (CAMGSD/IST)
The talk will be about joint work in progress with Janko Boehm (Saarbruecken) concerning the structure of Stanley--Reisner rings associated to cyclic polytopes. In more detail, denote by \Delta C_d(m) the boundary simplicial complex of the d-dimensional cyclic polytope which has m vertices....

Nonlinear elliptic problems for a class of anisotropic operators
Speaker: Agnese Di Castro (CMUC)
We present some existence and regularity results for nonlinear elliptic problems associated to a class of anisotropic operators, whose model is the anisotropic p-Laplacian. The results hold in a bounded domain and for Dirichlet boundary conditions....

Descent theory and stacks
Speaker: Filippo Viviani (CMUC)
Seminar of the working group on stacks...

Traces in Besov spaces
Speaker: Cornelia Schneider (CMUC)
We investigate Besov spaces with positive smoothness, obtained by different approaches. Using an equivalent atomic characterization for these spaces, we are able to study traces in different settings.The results we obtain are rather complete and extend the ones previously known to small...

Around the Toda lattice
Speaker: Khaoula ben Abdeljelil (Univ. de Poitiers, France)
We will show the Liouville integrability of differential equations that naturally appear on simple complex Lie algebras. ...

Local properties of non-negative solutions to some doubly non-linear degenerate parabolic equations
Speaker: Simona Fornaro (University of Pavia, Italy)
We study the local behavior of non–negative weak solutions of a wide class of doubly non-linear degenerate parabolic equations. We show, in particular, some lower pointwise estimates of such solutions in terms of suitable sub-potentials (dictated by the structure of the equation) and...

Grothendieck Topologies
Speaker: Ignacio Lopez (CMUC)

Diagonal minus tail forms and Lasserre's sufficient conditions for sums of squares
Speaker: Carla Fidalgo (ISEC)
By a "diagonal minus tail" form (of even degree) we understand a real homogeneous polynomialF(x_1,...,x_n)=F(X)=D(X)-T(X), where the diagonal part D(X) is a sum of terms of the form b_i x_i^{2d}with all b_i\geq 0 and the tail T(X) a sum of terms a_{i_1i_2...i_n}x_1^{i_1}......

Remarks on two commutators
Speaker: Tim Van der Linden (CMUC)
We show that two known conditions which naturally arose in commutatortheory and in the theory of internal crossed modules coincide: everystar-multiplicative graph is multiplicative if and only if every twoeffective equivalence relations commute as soon as so do theirnormalisations. This...

The Extended Toda hierarchy and Frobenius manifolds
Speaker: Guido Carlet (CMUC)
We will review the definition of Frobenius manifolds and give some hints of their connection with the theory of bi-Hamiltonian integrable equations, focusing on the example of the Extended Toda hierarchy and the quantum cohomology of the Riemann sphere....

Matrices, RSK correspondence and Kronecker products
Speaker: Ernesto Vallejo (Instituto de Matemáticas, UNAM)
In this talk we present an extension of the RSK and the dual RSK correspondence to 3-dimensional matrices. We apply this correspondence to obtain an algorithm that permits to compute, out a list of certain matrices, called minimal, several Kronecker coefficients for irreducible characters of...

Combinatorial aspects of Escher Tilings
Speaker: Srečko Brlek (LACIM/Universitè du Quèbec à Montrèal)
When Maurits Cornelis Escher started to produce astonishing tesselations of the plane in the late 30's, very few properties were known about theses. The ``simplest" tessellations make use of just one polygon or tile for tiling the entire plane, and the polygons that tile the plane by...

Reduction of Poisson-Nijenhuis Lie algebroids
Speaker: Antonio De Nicola (CMUC)

Examples of stacks
Speaker: Camille Laurent-Gengoux (CMUC)

What are sifted colimits?
Speaker: Jirí Adámek (TU Braunschweig, Germany)
Sifted colimits play in algebraic categories the analogous role that filtered colimits do in finitely presentable categories. A category D is called sifted if D-colimits commute with finite products in Set. Algebraic categories can be characterized as free completions of small categoris...

On étale morphisms in Algebra
Speaker: Maria Manuel Clementino (CMUC/Mat. FCTUC)
The inclusion of every monadic category over Set in its category of relational algebras, which is topological over Set, suggests the study of topological notions in this algebraic setting. In this talk we will present the algebraic study and behaviour of étale morphisms in this...

Fibered categories, part II
Speaker: Ignacio Lopez Franco (CMUC)

Complexity of Interior-point methods for solving convex conic feasibility problems with finite precision
Speaker: Vera Roshchina (University of Évora)
Polynomial complexity of interior-point methods (IPMs), as well as their practical efficiency have made them the methods of choice for solving a vast number of optimization problems. The first polynomial-time IPM was introduced by Karmarkar for Linear Programming, and later Nesterov and...

Fibered Categories
Speaker: Ignacio Lopez Franco (CMUC)
After learning about fibered categories and, in particular, categories fibered in groupoids, we will be able to attack the definition of a stack!...

On the complexity group of stable curves
Speaker: Margarida Melo (CMUC/Mat. FCTUC)
In 1969 Deligne and Mumford constructed a remarkable modular compactification of the moduli space of smooth curves of given genus, whose points parametrize stable curves. The geometry of this moduli space is very rich and its study has motivated the development of several important branches...

Relative commutator theory and the associator of loops
Speaker: Tim Van der Linden (CMUC/Mat. FCTUC)
The aim of this talk is to explain the concept of double central extension from the point of view of relative commutator theory. We shall focus on one concrete situation: the reflection of loops to groups. First we recall how the Galois theoretic approach to relative commutators arose out of...

Categories with colimits, 2-monads and Deligne's tensor product
Speaker: Ignacio Lopez Franco (CMUC/Mat.FCTUC)
I'll explain how every lax idempotent (=KZ) 2-monad has a canonical structure of a pseudo-commutative 2-monad. In the case of the 2-monad R whose algebras are categories with finite colimits, this gives rise to a (pseudo) monoidal structure on R-Alg, corresponding to a pseudo-closed...

A fundamental theory of linear transforms and applications to inverse problems
Speaker: Saburou Saitoh (Emeritus Professor of Gunma University, Japan, and University of Aveiro, Portugal)
In this lecture, I would like to introduce some fundamental theory for linear transforms in the framework of Hilbert spaces and its general applications with very concrete typical examples. The contents will be given by the following key words: Reproducing kernel, Pythagorean theorem,...

Morita equivalence or 2-categories : two point of views of Lie groupoids.
Speaker: Camille Laurent (CMUC/Mat. FCTUC)

Inner-derivations irreducible LY-algebras
Speaker: Pilar Benito (Universidade de Logronho, Espanha)
Lie-Yamaguti (LY-algebras) are binary-ternary algebras intimaly related to reductive homogeneous spaces. The LY-algebras which are inner-derivation-irreducible can be described through generalized Tits construction and non-associative systems such as Lie and Jordan algebras, Lie and...

Linear/Affine dependencies of (0,1) vectors
Speaker: Ilda Perez Silva (CELC/Mat. FCUL)
I will present and discuss recent results and conjectures concerning the following open problem: Is it possible to define the affine dependencies over the reals of the set Cn:={0,1}n in a purely combinatorial way, i.e. without any reference to the field R? More precisely, I will sketch the...

Rheological and multiscale FSI models for the numerical simulation of blood flow
Speaker: Alexandra Moura (IST, Lisboa)
The mathematical modelling and numerical simulation of the cardiovascular system is a very challenging task, due to its geometrical and functional complexity. Namely, in this lecture we address three main difficulties in this field. In particular, blood is a non-Newtonian shear-thinning...

Inner-derivation triple systems and Lie (super)algebras
Speaker: Pilar Benito (Universidade de Logronho, Espanha)
In 1985 J.R. Faulkner determine which 3-linear identities are satisfied by a large class of derivation-irreducible triple systems. The founded identities and related triples are in the heart of several well-known constructions of simple Lie algebras and superalgebras from Freudenthal to our...

Muckenhoupt weighted function spaces of Besov and Triebel-Lizorkin type: embeddings, traces, and singularities
Speaker: Dorothee D. Haroske (Friedrich-Schiller-Universität Jena, Germany)

Constructions of bipartite hypermaps
Speaker: Rui Duarte (Univ. Aveiro)
A hypermap is a cellular imbedding of a hypergraph on a surface. A hypermap is bipartite if we can divide its set of hypervertices in two parts in such a way that consecutive hypervertices around a hyperedge or a hyperface are contained in alternate parts. In this talk we will see some...

From medical imaging to clinical CFD
Speaker: Alberto Gambaruto (IST, Lisbon)
The talk will outline steps of how to obtain a virtual model from medical images, that can be used for numerical simulations. Steps of image enhancement, segmentation and interpolation, geometric modelling, mesh optimisation and surface smoothing are outlined. Numerical simulations for...

On the tropical Torelli map
Speaker: Filippo Viviani (CMUC/Roma Tre)
The classical Torelli map is the modular map from the moduli space of curves of genus g to the moduli space of principally polarized abelian varieties of dimension g, sending a curve into its Jacobian. The Torelli map is known to be injective (Torelli theorem) and the image has been...

On the equations of viscoelastic diffusion in polymers
Speaker: Dmitry Vorotnikov (CMUC - Universidade de Coimbra)
We shall consider the system of PDEs which models the non-Fickian anomalous (viscoelastic) diffusion of a penetrant liquid in a polymer. Recent results on existence, uniqueness and attractors for various types of generalized solutions to the corresponding boundary value problems will be...

Local homeomorphisms in monadic categories
Speaker: Maria Manuel Clementino (CMUC/Mat. FCTUC)

The equivalence between groupoids and crossed modules from a categorical point of view, with application in the case of groups
Speaker: Nelson Martins-Ferreira (CDRSP/IPLeiria)
Starting with the well known equivalence of internal groupoids and crossed modules, in the case of groups, involving also the equivalence between points and actions, and the adjunction between actions by conjugation and semidirect products, we consider the problem of finding an appropriate...

On the representation of archimedean f-rings: extended versus pointfree functions
Speaker: Bernhard Banaschewski (McMaster University, Canada)
A systematic comparison of the classical representation of archimedean f-rings with unit as l-rings of extended real-valued continuous functions (=allowing infinite values) on some compact Hausdorff spaces and their more recent representation as l-rings of real-valued continuous functions in...

Chirality under a combinatorial point of view
Speaker: António João Breda (Univ. Aveiro)
Although the phenomenon of chirality appears in many areas of science, specially in chemistry, in mathematics it appears essentially in topological, geometrical and combinatorial forms. Chirality in maps and hypermaps (combinatorial and algebraic form of chirality) is not merely a binary...

A reduced basis multiscale method
Speaker: Christophe Prud'homme (Université de Grenoble, France)
We are interested in the two following model problems:The first equation is a diffusion equation with variable coefficients which models many problems such as the prediction of the presence of oil or gaz in porous media. u is then the pressure of the fluid and represents the permeability of...

Fourier-Mukai transforms and moduli spaces of semistable sheaves for genus 1 curves
Speaker: Ana Cristina López Martín (Univ. Salamanca, Spain)
Since its introduction, the Fourier-Mukai transform has been a very important tool for the study of the properties of moduli spaces of sheaves and vector bundles. For instance, Atiyah's characterization of vector bundles allowed Tu to give a geometric description of the moduli spaces of...

Interior point methods for complementarity problems
Speaker: Florian Potra (University of Maryland Baltimore County, USA)
Complementarity is ubiquitous in the natural and social sciences. It is a fundamental principle underlying equilibrium. In a primal-dual description of a system it means that either the primal or the corresponding dual component of the solution vector must vanish. There are many problems...

Dynamics of linear operators
Speaker: Özgür Martin (Bowling Green State University, Ohio, USA)
An intriguing result of G. D. Birkhoff states that there exists an entire function $f$ whose translates $f(z+n), n ≥0$ can approximate any entire function, uniformly on compacts sets. In 1952, as a similar result, G. R. MacLane showed existence of an entire function whose derivatives form...