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Main Seminar on Stacks Lab for Computational Mathematics Research Seminar Program - UC|UP MATH PhD Program Thematic Line - History of Mathematics UC|UP MATH PhD Program
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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 (positive...
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 using...
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 testing...
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. We...
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 two...
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 description...
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 sublocales...
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 semigroups. Many...
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 present...
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 inferred...
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. Volkov,...
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 hypermaps...
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 theory...
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 (x°y=xy+yx)....
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 an...
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 theory,...
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 the...
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 coalgebra has a...
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 matrices, the...
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 quantum...
An introduction to L_\infty algebras and L_\infty algebroids
Speaker: Raquel Caseiro (CMUC/Univ. Coimbra)
L∞ 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 one asks it to...
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 of...
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 Lawvere,...
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) can be...
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 immediately...
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 expectation is...
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 structure...
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 almost...
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 numerical...
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 possible for...
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 S-protomodular...
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 interesting...
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 their...
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 of...
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 talk I will...
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 global...
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 and...
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 unified...
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 some...
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 classical...
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 version for...
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 are...
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 the...
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 geometric...
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 applications...
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 type....
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 algorithms...
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) and the...
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 algebra...
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 monomials....
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 population ui...
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 results of...
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 categorical...
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 case, we...
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 solutions...
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 the...
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 able to...
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 of...
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 smoothness....
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 facilities.In...
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 replace...
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 many...
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 concrete for...
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 context...
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. Despite...
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 Quantum...
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 an...
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 its...
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 commonly...
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 detailed...
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, the...
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 the...
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 is joint...
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 those...
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 semigroup...
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 that it...
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 dPIV....
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 problems...
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 suitably...
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 but for...
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 obtained...
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 under...
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 talk...
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 explicit...
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 algebroids,...
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 promising...
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 presents the...
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 there is a...
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 notion...
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 context...
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 techniques are...
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 different...
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 mathematical...
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 manifold is...
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 ideas...
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 fibration of...
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 of finite...
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 Thomas...
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 homology and...
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 structure....
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 one...
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 based on...
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 standard...
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 quantitatively...
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 Problem...
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 divisibility....
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 differences...
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 multiplicity...
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 different ways...
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 medicine....
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 $\alpha.$...
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 and the...
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 chemical...
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 with...
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 for...
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 abelian...
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 are...
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 fibred Lie...
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 plane...
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 results....
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 map in a...
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 it to...
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 with...
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 dually...
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 first...
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 equals...
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 twisted...
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 weak)...
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 are...
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 between...
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 initial...
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 functions on...
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 combined...
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 image...
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 category,...
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 model....
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 tangent bundle TM....
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 results...
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 same...
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 to World...
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 answer for...
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 Ping Xu....
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 involving...
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 question that...
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 description...
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 respect...
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, Aldo...
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 increasing...
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 space. The...
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 energy...
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 which...
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 tem ...
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 of...
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 signals...
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 discrete...
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 address the...
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 a...
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 are...
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 pointfree...
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 with...
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 representations of...
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 difficulties show...
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 approximants...
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 different...
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 the...
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 basic...
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 index...
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 simple...
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 functions,...
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 equipped with...
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 in...
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 of the...
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 symmetries, etc....
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 to obtain...
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 actions, or...
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 established a...
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 conditions...
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 X and G....
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 the...
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 naturally...
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 characterise in...
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. In the...
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 problems,...
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. Everaert, M....
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 Topology, A...
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 which...
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 relevance of...
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 consist of a...
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 of...
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 continuous real...
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 linearly...
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 theorem...
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 hypergeometric...
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 Kan-injective hulls...
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 resulting...
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 biodegradable...
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. We also...
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 prove...
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 under...
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. Outside the...
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 property that...
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 evolving...
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 of...
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 counting...
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 rates for...
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 DGTD...
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 prove the...
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, or in...
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 recent...
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 hard...
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 groups,...
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 leads...
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 survey on...
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 complexity of a...
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 nonlocal...
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 curves,...
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 functions...
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 sphere....
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, electrons)...
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 structures of...
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 important...
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 five...
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 unique...
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 measurements are...
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  (independent of...
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 upper bound...
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 singularities, then...
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 for which...
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 field. The...
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 (M,\omega).I...
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 the...
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 other.We...
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 spaces...
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, for a...
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 composition. The...
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 "Fer...
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 closure...
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 necessarily...
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 and...
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 is the...
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 the...
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 of...
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 into play....
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 equations in...
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 this...
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 also...
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 partial...
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 unstructured...
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 that the...
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 constant scalar...
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 yet no...
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 derivative-free...
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 necessidade de...
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 of a...
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 integrability of...
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 enhance the...
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 compact...
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) | p,q in...
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 developed...
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 of...
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, they have...
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 of...
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 spatiality...
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 recolorization...
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 equivalence of...
3 ×3 matrices with a flat portion on the boundary of the numerical range
Speaker: Fatemeh Esmaeili Taheri (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 number...
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 prove the...
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 problem...
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 algebras...
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 out by...
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 the...
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 well...
(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 some...
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 myself,...
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 matrices...
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 the...
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 to...
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 semigroups of a...
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 of a...
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 metric in an...
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 or simple...
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 are...
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 augmented...
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 to smooth...
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 completion...
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 ones and...
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 notion...
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 variables. In...
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 modeling...
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 , any...
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 simple...
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, such as...
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 will...
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 takes...
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 construction of...
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 theorem for...
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 will...
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 analytic...
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. Lie...
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 of the...
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 molecular weight...
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 the...
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 a...
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 between the...
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, we...
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 a...
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 fibrations,...
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. To...
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 about...
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 the...
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 interpolation...
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 evaluate...
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 objects...
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 of ...
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 diagnostic...
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 are...
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 discontinuity,...
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 characteristic...
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 work of...
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 to...
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 these...
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 the...
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, the...
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 answer to...
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 deformation...
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 structural...
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 smoothness s...
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 finite set....
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) bundles....
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 general ...
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) denotes the...
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 algorithm...
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 path from...
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 complex...
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 maximal...
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 (i.e....
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 degenerate by...
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 finite...
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 study...
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 family...
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 the image...
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 [O]. P....
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 stack...
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 series...
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 direct...
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 discuss...
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 a proof...
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 hyperplane...
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 the...
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 geometry.In...