Centre for Mathematics, University of Coimbra

The question of how to decompose a Specht module, for an arbitary diagram, into irreducible submodules, is not yet known. Similar question for Schur functions for arbitrary diagrams. We discuss known results for skew shapes, in particular, border strips, or forests, and the role of R. Liu's...

Maths for crime prediction
2019-12-11

Speaker: Adérito Araújo (CMUC, Univ. Coimbra)

It is undeniable that an unfortunate aspect of modern life, technologically and economically more developed, is the presence of crime distributed in major urban areas. This does not only affect countries like Portugal or the European continent, but is experienced in all countries around the world....

The moduli spaces of Higgs bundles
2019-12-02

Speaker: André Oliveira (CMUP)

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

Emergence of strange attractors from singularities
2019-11-27

Speaker: Alexandre Rodrigues (CMUP, FCUP)

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

Corruption cycles in democracy
2019-11-13

Speaker: Alberto Adrego Pinto (FCUP)

In this talk, with the goal of analysing the evolution of corruption, we introduce an evolutionary game theoretic dynamical model describing the interaction of citizens with government and officials or bureaucrats of the state in a democratic country.We study and interpret the socio-political and...

Dynamical systems from mutation-periodic quivers: definition and reduction by pre-symplectic tools
2019-11-06

Speaker: Inês Cruz (CMUP, FCUP)

Cluster algebras and their associated quivers were introduced in 2002 by Fomin and Zelevinsky to provide a framework to study total positivity in matrix groups. Since then, cluster algebras have been successfully linked to a wide range of subjects including Poisson geometry, integrable systems,...

Some challenging problems on numerical semigroups
2019-10-30

Speaker: Manuel Delgado (CMUP, Univ. Porto)

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

Differential equations with two time-scales
2019-10-30

Speaker: Isabel Labouriau (CMUP, Univ. Porto)

I'll discuss the role of different time-scales in differential equations and the associated geometry. This will be illustrated by a simple example, the FitzHugh-Nagumo equations, and by two of these equations coupled to form a system in ${\mathbb R}^4$. When two different time-scales are considered...

Frankl Conjecture
2019-10-23

Speaker: André Carvalho (UC|UP PhD student)

This seminar will deal with a conjecture proposed in 1979 by Peter Frankl related to union-closed families of sets. Despite the fact that the conjecture regards finite union-closed families of sets, which appear to be very simple objects, very little is known about them. We try to present in detail...

Categorical semantics of intuitionistic linear logic
2019-10-23

Speaker: Carlos Fitas (UC|UP PhD student)

The Curry-Howard-Lambek correspondence shows the deep connection between programs, proofs and morphisms in closed cartesian categories. It's natural to ask if similar results are true in other logics. Identifying the intuitionistic linear logic derivations up to the transformations in cut...

An ageing ordering
2019-10-16

Speaker: Beatriz Santos (UC|UP PhD student)

Many classes of lifetime distributions are characterized by their ageing properties, that can be described by their survival functions or by their failure rate functions. These ageing properties allow us to compare two distributions within the same family, giving rise to ageing orderings. The aim of...

Ergodic theorems from topological and probabilistic viewpoints
2019-10-16

Speaker: Lucas Amorim (UC|UP PhD student)

Ergodic theorems are classic measure theoretical results in dynamical systems or, more precisely, ergodic theory. They state that convergence of Birkhoff averages is typical, in a measure theoretical sense. This work aims to explain how these results can be reìnterpreted in light of topology...

Deep learning meets PDEs: an effective framework for image restoration
2019-10-09

Speaker: Sílvia Barbeiro (CMUC, Univ. Coimbra)

Image restoration is one of the major concerns in image processing with many interesting applications. Partial differential equation (PDE) based models, namely of nonlinear diffusion type, are well-known and widely used for image noise removal. In this seminar we will describe a flexible learning...

Algebras associated to quivers
2019-10-02

Speaker: Rui Prezado (UC|UP PhD student)

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

Spectral analysis in the study of dynamical systems
2019-10-02

Speaker: Raquel Couto (UC|UP PhD student)

After a brief journey into a class of Symbolic Dynamical Systems, that is related to Markov Chains, I will present the Limit Theorem for Markov Chains which can be obtained as a corollary of Perron Theorem (a spectral theorem in linear algebra). Next, we will see what may be taken as a...

Coupled cell networks and systems
2019-09-25

Speaker: Ana Paula Dias (CMUP)

The aim of this talk is to introduce the connection between coupled cell networks and coupled cell systems. We also plan to address the issue of classifying networks from the dynamics point of view. The seminar takes place in PORTO....

Truncated boolean representable simplicial complexes
2018-12-12

Speaker: Pedro V. Silva (CMUP, Univ. Porto)

These structures constitute the largest known class of simplicial complexes admitting a geometric/topological theory. We will present the main features of this class and some recent results (joint work with Stuart Margolis (Bar-Ilan) and John Rhodes (Berkeley))....

Superalgebras with superinvolution
2018-12-12

Speaker: Herlisvaldo Costa Santos (UC|UP PhD programme student)

Our objective in this work is to provide primitive associative superalgebras a structure analogous to those for the algebras and to classify primitive superalgebras with superinvolution having a minimal superideal....

Representation type of algebras and quivers
2018-12-05

Speaker: Ivan Yudin (CMUC, Univ. Coimbra)

One of the first results one encounters in the standard university courses of algebra are classifications of equivalence classes of matrices under various transformations. If we are allowed to multiply the matrix in question from each side with an invertible matrix, then the corresponding...

A mathematical model for a plant circadian oscillator
2018-11-28

Speaker: Adérito Araújo (CMUC, Univ, Coimbra)

Circadian rhythms are generated at the cellular level by a small but tightly regulated genetic network. They are observed in most organisms on earth and are known to play a major role in successful adaptation to the 24-h cycling environment. Understanding the molecular basis of cellular oscillations...

On the existence of solutions for inextensible string equations
2018-11-23

Speaker: Ayk Telciyan (UC|UP PhD programme student)

In this talk, we analyze existence of solutions for inextensible string equations. In particular, we have results in two directions.On one hand, we find explicit traveling wave solutions for a system of hyperbolic conservation laws resulting from inextensible string equations via suitable change of...

Representations of fundamental groups of surfaces
2018-11-23

Speaker: Peter Gothen (CMUP, Univ Porto)

We consider representations of the fundamental group of a closed surface in the group SL(2,R). To each such representation one can associate an integer invariant called the Toledo invariant. A theorem of J. Milnor says that the absolute value of the Toledo invariant is less than or equal to g-1,...

Campanato spaces and applications in partial differential equations
2018-11-23

Speaker: David Jesus (UC|UP PhD Programme student)

In this talk I will discuss a generalization of Campanato's characterization of Holder continuity, and use these results to study the regularity of solutions to the non-homogeneous p-Laplace equation....

Boolean representable simplicial complexes
2018-11-23

Speaker: Maria Inês Couto (UC|UP PhD Programme student)

In this seminar we will discuss some properties of a particular class of simplicial complexes from a purely combinatorial perspective. The elements of this class, including all the matroids, admit a representation by a matrix with entries in the boolean semiring, so they are said boolean...

Actions of Hopf algebras
2018-11-16

Speaker: Christian Lomp (CMUP, Univ Porto)

Group algebras and enveloping algebras of Lie algebras are examples of Hopf algebras. Automorphisms acting on rings as well as derivations acting on them are examples of Hopf algebra actions. Guided by these classical examples, we will motivate the study of Hopf algebra actions and consider in...

Categories, allegories
2018-11-14

Speaker: Igor Arrieta (UC|UP PhD programme student)

A binary relation from a set A to a set B is a subset of the cartesian product AxB. Moreover, a function f: A->B can be identified with a particular type of relation, namely the relation consisting of pairs (x,f(x)). Consequently, the usual category of sets can be regarded as a subcategory of...

Geodesics in the space of Kähler metrics
2018-11-14

Speaker: Pedro Silva (UC|UP PhD programme student)

A Kähler manifold is a differentiable manifold with three geometric structures: a Riemannian metric, a symplectic form, and a complex structure, satisfying some compatibility conditions. The metrics and the symplectic forms for which these compatibility conditions are satisfied are called...

Identification and simulation of flow in heterogeneous media: a model for oil extraction
2018-11-14

Speaker: Hugo Peña Gomez (UC|UP PhD Programme student)

The models of double porosity-permeability are used to described the dynamics of oil extraction (porous medium). The talk will be about presenting some aspects of this kind of models and a variation considering a particular medium structure. Some numerical results will be exposed. ...

On the group of a rational maximal bifix code
2018-11-07

Speaker: Alfredo Costa (CMUC, Univ. Coimbra)

A code is a set of words that freely generates a free submonoid of the free monoid. A specially relevant place in the theory of codes is occupied by the maximal bifix codes.In the last years, attention has been given to a process of "localization" in which one looks at the intersection of...

What is ... Pointfree Topology?
2018-10-31

Speaker: Jorge Picado (CMUC, Univ. Coimbra)

Pointfree topology deals with frames and locales, the pointfree counterparts of topological spaces. We shall present motivation for this approach to topology and its basic features and facts. We will emphasize some of the main differences between the two approaches and some advantages of the...

3-manifolds, knots and surfaces
2018-10-24

Speaker: João Miguel Nogueira (CMUC, Univ. Coimbra)

We will survey the motivation and history of 3-manifold topology, together with its twin subject of knot theory, giving special emphasis to the importance of surfaces on the understanding of these subjects. Under this framework, we will also review contributions of the speaker as suitable. ...

Applied Mathematics: applications in biomedicine and biomathematics
2018-10-17

Speaker: Isabel Narra de Figueiredo (CMUC, Univ. Coimbra)

This talk focus on the description of some computer-assisted methods we have developed for the automatic interpretation of medical images and on some biomathematics models we have proposed to represent and simulate the early stages of colon cancer....

Computing the indecomposable representations of left regular bands
2018-10-10

Speaker: Herman Goulet-Ouellet (UC|UP PhD programme student)

Left regular bands are a family of semigroups that enjoy many surprising properties. They have received some attention recently due to their link with Markov chains and hyperplane arrangements. In this talk, we will see how to compute the indecomposable projective representations of finite left...

The boolean reflection of a frame and the Cantor-Bendixson derivative
2018-10-10

Speaker: Ana Belén Avilez (UC|UP PhD programme student)

We consider two categories, the category of frames and the category of complete boolean algebras. We know that a complete boolean algebra is always a frame, but we want to assign universally a complete boolean algebra to each frame. It turns out this is not always true, but there is a result that...

Optimal transport, PDEs and geometry
2017-04-05

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...

An introduction to Sasakian manifolds
2017-03-22

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...

On the construction of complex algebraic surfaces
2017-03-08

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
2017-03-08

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
2017-02-22

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
2017-02-22

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...

The combinatorics of noncrossing and nonnesting partitions
2017-02-08

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
2017-02-08

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...

Castelnuovo-Mumford regularity and graph invariants
2016-12-16

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....

On Taken's Last Problem: times averages for heteroclinic attractors
2016-12-02

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
2016-12-02

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...

Smoothness Morrey spaces and their envelopes
2016-11-18

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
2016-11-18

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....

A successful pair: symbolic dynamics and (pro)finite semigroups
2016-11-04

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
2016-11-04

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
2016-10-28

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
2016-10-28

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...

A fractional diffusion model with resetting
2016-10-14

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
2016-10-14

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...