# Seminars

Speakers:
Margarida Mendes Lopes
Date: Friday, 3 March, 2017
Abstract:

Let S be a smooth projective surface over C and B a smooth projective curve. A fibration f : SB is a surjective morphism such that the general fibre is a smooth connected curve.

This talk will focus on some properties of fibrations with general fibre of genus ≥ 2, discussing in particular the existence and number of singular fibres on a fibration.

Speakers:
Célia Borlido
Date: Monday, 20 February, 2017
Abstract:

In 2008, Gehrke, Grigorieff, and Pin proposed Stone duality as a means for studying Boolean algebras of (non-necessarily regular) languages. They showed how that tool could be understood as a generalization of some key concepts found in the study of varieties of regular languages, such as the syntactic monoid of a language. In this talk, I will present the main points of this approach.

Speakers:
Tara Brough
Date: Friday, 10 February, 2017
Abstract:

Let FIM(X) be the free inverse monoid on a finite set X. The word problem of FIM(X) is easily seen to be recognisable in linear space (e.g. using Munn trees), and this has been improved to log space (Lohrey and Ondrusch 2007).

Speakers:
Emilio Franco
Date: Friday, 10 February, 2017
Abstract:

Let Λ be a D-algebra in the sense of Bernstein and Beilinson. Higgs bundles, vector bundles with flat connections, co-Higgs bundles... are examples of Λ-modules for particular choices of Λ. Simpson studied the moduli problem for the classification of Λ-modules over Kähler varieties, proving the existence of a moduli space of Λ-modules. Using the Polishchuck-Rothstein transform for modules of D-algebras over abelian varieties, we obtain a description of the moduli spaces of Λ-modules of rank 1. We also proof that polystable Λ-modules decompose as a direct sum of rank 1 Λ-modules.

Speakers:
Teruhiko Soma
Date: Friday, 3 February, 2017
Abstract:

Takens' last problem. Whether are there persistent classes of smooth dynamical systems such that the set of initial states which give rise to orbits with
historic behavior has positive Lebesgue measure?

Speakers:
Shin Kiriki
Date: Friday, 3 February, 2017
Abstract:

Colli-Vargas' conjecture. Every two-dimensional diffeomorphism with homoclinic tangency can be approximated in the Cr-topology by diffeomorphisms
having non-trivial wandering domains.

Speakers:
Roger Picken
Date: Friday, 3 February, 2017
Abstract:

Non-abelian gerbes are a generalization of principal G-bundles, involving the replacement of the Lie group G by a Lie 2-group, or crossed module of groups, not necessarily Abelian. Apart from providing a nice example of categorification in geometry, they have found a number of applications in physics, e.g. in higher gauge theory and topological states of matter.

Speakers:
Filippo Viviani
Date: Friday, 27 January, 2017
Abstract:

We generalize the classical MacDonald formula for smooth curves to reduced curves with planar singularities. More precisely, we show that the cohomologies of the Hilbert schemes of points on a such a curve are encoded in the cohomologies of the fine compactified Jacobians of its connected subcurves, via the perverse Leray filtration. A crucial step in the proof is the case of nodal curves, where the weight polynomials of the spaces involved can be computed in terms of the underlying dual graph. This is a joint work with Luca Migliorini and Vivek Schende.

Speakers:
Margarida Melo
Date: Friday, 27 January, 2017
Abstract:

Among abelian varieties, Jacobians of smooth projective curves C have the important property of being autodual, i.e., they are canonically isomorphic to their dual abelian varieties. This is equivalent to the existence of a Poincaré line bundle P on J(C)×J(C) which is universal as a family of algebraically trivial line bundles on J(C). A yet other instance of this fact was discovered by S. Mukai, who proved that the Fourier-Mukai transform with kernel P is an auto-equivalence of the bounded derived category of J(C).

Speakers:
Rui Albuquerque
Date: Friday, 20 January, 2017
Abstract:

We present a recent result about the Riemannian metric structure of the tangent manifold TM, the total space of the tangent bundle T M → M of any given Riemannian manifold M. We recall how such space is endowed with a metric, due to S. Sasaki, and which are its main properties. Following this, we show the construction of a fully original Hermitian structure, called ciconia, which leads to interesting Kähler-Einstein and, in particular, non-compact Calabi-Yau manifolds.

Speakers:
Lorenzo Díaz
Date: Friday, 13 January, 2017
Abstract:

Estudaremos produtos tortos transitivos modelados sobre um "shift" completo cujas funções nas fibras estão definidas no círculo e têm
simultaneamente regiões de contração e de expansão. Introduziremos uma série de axiomas na dinâmica das fibras que capturam os mecanismos
essenciais das dinâmicas robustamente transitivas com fibras compactas. As dinâmicas obtidas são genuinamente não-hiperbólica e possuem simultaneamente medidas ergódicas com entropia positiva com expoentes de Lyapunov positivos, negativos e nulos.

Speakers:
Edson Vargas
Date: Friday, 13 January, 2017
Abstract:

Estudamos medidas invariantes para os fluxos de Cherry, isto é: fluxos no toro bidimensional que possuem uma sela, uma fonte, e nenhum outro ponto fixos, órbitas fechadas ou conexões de sela. No caso em que a sela é dissipativa ou conservativa nós mostramos que as únicas medidas invariantes são as medidas de Dirac suportadas nos dois pontos fixos e a medida de Dirac na sela é uma medida física.

Speakers:
Katrin Gelfert
Date: Friday, 20 January, 2017
Abstract:

Estudaremos conjuntos hiperbólicos invariantes de certos produtos tortos com expansão uniforme nas fibras e com difeomorfismos hiperbólicos de superfície na base. Assim, estes conjuntos são gráficos invariantes. Em geral estes gráficos são ou (em casos não genéricos") Lipschitz contínuos ou genuinamente Hölder contínuos.  No caso não-Lipschitz sua estrutura fractal é de interesse natural, estudaremos sua dimensão box-counting.

Speakers:
Carlos Florentino
Date: Friday, 6 January, 2017
Abstract:

A complex reductive algebraic group G has a special kind of mixed Hodge structure which is called Hodge-Tate type. These structures can then be described by their E-polynomial (or Hodge-Euler polynomial), which in turn is related to counting polynomials for the number of points of G in finite fields.

Speakers:
Jaime Silva
Date: Friday, 6 January, 2017
Abstract:

Introduced by Deligne, mixed Hodge structures provide a generalization of the Kähler decomposition of cohomology. They were motivated by Deligne’s attempt to assign “virtual” Hodge numbers to singular varieties, a problem in turn related to the Weil conjectures.

Speakers:
Ricardo Campos
Date: Thursday, 5 January, 2017
Abstract:

Graph complexes are differential graded vector spaces whose elements are linear combinations of combinatorial graphs with a differential given by some combinatorial rule such as contraction of edges.
Many mathematical problems admit formulations in terms of graph complexes, in topics as distinct as knot theory, outer automorphisms of free groups and moduli spaces of curves.

Speakers:
Date: Friday, 16 December, 2016
Abstract:

This is your chance to get to know some of the work done at CMUP in these four research lines:

• Computational Mathematics
• Dynamical Systems
• Mathematical Models and Applications
•  Semigroups, Automata and Languages

Friday, December 16th (2016) in

Timetable

14h00 – 14h20: Maria Carvalho

Random Battles on Free Worlds

14h30 – 14h50: Ana Paula Tom ́as

On Visibility and Surveillance Problems

15h00 – 15h20: Filomena Dias D’Almeida

Speakers:
Helena Reis
Date: Thursday, 15 December, 2016
Abstract:

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 dimension of M
solely. However several important problems arise once specific constraints are imposed on the manifold M.
For example, the case of homogeneous manifolds has been intensively studied in connection with which is

Speakers:
Claude Marion
Date: Monday, 5 December, 2016
Abstract:

In the 1980s, following the classification of   finite simple groups, it was established that every finite simple group can be generated by two elements. A natural question arises: can we impose restrictions on these generators? Given a triple (a,b,c) of positive integers, we say that a finite group is an (a,b,c)-group if it can be generated by two elements of respective orders dividing a and b,  and having product of order dividing c. In other words, an (a,b,c)-group is a finite quotient of the triangle group

Speakers:
Gill Barequet
Date: Wednesday, 23 November, 2016
Abstract:

A polyiamond is an edge-connected set of cells on the triangular
lattice.
The size of a polyiamond is simply the number of cells it contains.
The growth constant of polyiamonds, $\lambda_T$, is the limit of the
ratio between the number of polyiamonds of size n+1 and the number of
polyiamonds of size n, as n tends to infinity.  In this talk I will show
improved lower and upper bounds on $\lambda_T$, proving that it is
between 2.8424 and 3.6050.

Speakers:
Manuel José Ribeiro de Castro Silva Martins
Date: Tuesday, 29 November, 2016
Abstract:

Ore extensions provide a way of constructing new algebras from preexisting ones, by adding a new indeterminate subject to commutation relations. A recent generalization of this concept is that of double Ore extensions. On the other hand, Hopf algebras are algebras which possess a certain additional dual structure. The problem of extending a Hopf algebra structure through an Ore extension has been discussed in a recent paper by Brown, O'Hagan, Zhang and Zhuang, of which we present the main result.

Speakers:
António Breda D’azevedo
Date: Thursday, 17 November, 2016
Abstract:

Regular maps consist of triples $(G,a,b)$ where $G$ is a finite group and $(a,b)$ is a pair of generators of $G$ such that the product $ab$ is 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 $\overline{{\cal M}}=(G,a^{-1},b^{-1})$.

Speakers:
Tamas Hausel
Date: Monday, 28 November, 2016
Abstract:

Motivated by the work of Gukov and Du Pei we discuss a construction of a Frobenius algebra, which computes equivariant indices of line bundles on the moduli space of Higgs bundles. This is joint work with Andras Szenes.

Speakers:
Paulo Varandas
Date: Friday, 11 November, 2016
Abstract:

One of the main purposes of dynamical systems is to understand the behavior of the space of orbits of maps and flows on compact metric spaces. It is often the case that we refer to chaotic dynamical systems whenever it presents dense regular behavior (e.g. periodic) and sensitivity to initial conditions.

Speakers:
Fernando Lucatelli Nunes
Date: Friday, 25 November, 2016
Abstract:

I will talk about a basic procedure of constructing adjunctions, sometimes called Kan construction/adjunction. In the first part of the talk, I will construct abstractly such adjunctions via colimits. In the second part, we give some elementary examples: fundamental groupoid, sheaves, etc. We assume elementary knowledge of basic category theory (definition of categories, colimits and Yoneda embedding).

Speakers:
Pier Giorgio Basile
Date: Friday, 25 November, 2016
Abstract:

In Category Theory there is a well developed theory of monads, proved to be very useful for 1-dimensional universal algebra and beyond. The relation between adjunctions and monads was first noticed by Huber (Homotopy Theory in General Categories): every adjunction gives rise to a monad. Then, Eilenberg, Moore and Kleisli realized that every monad comes from an adjunction. In particular, Eilenberg and Moore (Adjoint Functors and Triples) realized that, for every monad T, there is a terminal adjunction (called Eilenberg-Moore adjunction) which gives rise to T.

Speakers:
Alberto José Hernandez Alvarado
Date: Friday, 25 November, 2016
Abstract:

In this conference, I will be reviewing the main aspects of my thesis dissertation. I will introduce the notion of depth of a ring extension $B\subseteqA$ and give several examples as well as important results of recent years. I will then consider a finite dimensional Hopf algebra extension $R \subseteq H$ and its quotient module $Q := H/R^+H$ and show that the depth of such an extension is intrinsically connected to the representation ring of $H, A(H)$. In particular, we will see that finite depth of the extension is equivalent to the quotient module $Q$ being algebraic in $A(H)$.

Speakers:
Antonio Macchia
Date: Friday, 25 November, 2016
Abstract:

We define the order relation given by the proper divisibility of monomials, inspired by the definition of the Buchberger graph of a monomial ideal. From this order relation we obtain a new class of posets. Surprisingly, the order complexes of these posets are homologically non-trivial. We prove that these posets are dual CL-shellable, we completely describe their homology (with integer coefficients) and we compute their Euler characteristic. Moreover this order relation gives the first example of a dual CL-shellable poset that is not CL-shellable.

Speakers:
Teresa Monteiro Fernandes
Date: Friday, 18 November, 2016
Abstract:

In this talk I will give an overview of the main concepts and results in D-module theory, and then switch to the notion of relative D-module. I will explain the main motivation for the study of holonomic relative modules given by Mochizuki's notion of mixed twistor D-module. We will explain the Riemann-Hilbert correspondence in this case as a joint work with Claude Sabbah.

Speakers:
Nuno Bastos
Date: Friday, 4 November, 2016
Abstract:

In this talk we deal with fractional differential equations, with dependence on a Caputo fractional derivative. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional differential equations may model more efficiently certain problems than ordinary differential equations [1].

[1] R. Almeida, N.R.O. Bastos and M.T.T. Monteiro,  Modelling some real phenomena by fractional differential equations. Math. Meth. Appl. Sci. (39) No 16, 4846-4855 (2016)

Speakers:
Xavier Roulleau
Date: Friday, 11 November, 2016
Abstract:

A smooth cubic hypersurface X of dimension >1 is unirational. The variety of lines F(X) on these hypersurfaces is an essential tool to understand the geometry of X. In dimension 3, the study of F(X) enables to prove that X is always irrational.

In this talk we study the zeta function of F(X) and we obtain a simplified proof of the irrationality of a dense set of smooth cubic threefold. This is a joint work with D. Markouchevitch.

Speakers:
Giuseppe Pontrelli
Date: Thursday, 3 November, 2016
Abstract:

In this talk I will present a mathematical model  describing the dynamics of a substance between a two-layer media of different properties and extents.

The model incorporates drug diffusion, dissolution and solubility  in the polymer coating, coupled with diffusion, convection and reaction in the biological tissue.  Each layer contains bound and free drug phases so that the resulting model is a coupled two-phase two-layer system of partial differential equations.

Speakers:
Juliane Oliveira
Date: Friday, 28 October, 2016
Abstract:

This work is related to the study of pattern formation in symmetric physical systems. Our purpose is to discuss a possible model, namely the projection model, to explain the appearance and evolution of regular patterns in symmetric systems of equations.

Results found in Crystallography and Equivariant Bifurcation Theory are used extensively in our work. In particular, we provide a formalism of how the model of projection can be used and interpreted to understand experiments of reaction-diffusion systems.

Speakers:
Giovanna Guaiana
Date: Thursday, 20 October, 2016
Abstract:

The study of the trace monoid was initiated by A. Mazurkiewicz in 1977, and it was later developed, motivated by its interpretation as a model to describe the behaviour of concurrent systems. When a partial commutation (often called independence relation) is fixed over the letters of an alphabet, stating what letters can commute, a trace can be identified with an equivalence class of words that can be obtained from one another by switching successively some consecutive independent letters.

Speakers:
Oscar García-Prada
Date: Friday, 7 October, 2016
Abstract:

We consider the action of the mapping class group of a compact  surface S of genus g>1 on the character variety of the fundamental group of S  in a connected semisimple real Lie group G.

Speakers:
Marco Martins Afonso
Date: Friday, 30 September, 2016
Abstract:

We show some analytical, and partly numerical, results on the effective diffusivity of tracer and inertial particles in flowing fluids. Particle diffusion is a phenomenon where the mean square displacement - after subtracting its average, which corresponds to the advective or ballistic degree of freedom - follows a power law in time. In most standard cases the exponent is 1, and the tensorial prefactor is called "eddy diffusivity" and can be found by means of a multiple-scale expansion. If under investigation are tracers, i.e.

Speakers:
António Sodré
Date: Friday, 23 September, 2016
Abstract:

Deterministic dynamics on stationary point process in Rd 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 distributions of point process given there is a point of the nth iteration of the point-shift at the origin. We will introduce the notion of marked stochastic point-shifts.

Speakers:
José Mourão
Date: Friday, 23 September, 2016
Abstract:

The geodesics for the Mabuchi metric on the space of Kaehler metrics on a manifold correspond to solutions of the homogeneous complex Monge-Ampere (HCMA) equation. We will describe a method for reducing the Cauchy problem for the HCMA equation with analytic initial data to finding a related Hamiltonian flow followed by a "complexification". Examples and applications will be discussed.

Work in collaboration with J.P. Nunes and T. Reis

Speakers:
Flora Ferreira
Date: Friday, 8 July, 2016
Abstract:

Stable solutions of an integro-differential equation (known as “Amari equation”) have been proposed as a model of a neural population representation of remembered external stimuli.  In this talk I will present the study of the conditions that guarantee the existence and stability of multiple regions of high activity or ‘‘bumps’’ in a one dimensional, homogeneous neural field with localized inputs. These multi-bump solutions represent the core of an original dynamic field model of fast sequence learning that was developed and tested in a robotics experiment.

Speakers:
Cristiana J. Silva
Date: Friday, 1 July, 2016
Abstract:

In a first part, we consider a Tuberculosis (TB) model with time delays in both state and control variables, representing the time delay on the diagnosis and commence- ment of treatment of individuals with active TB infection, respectively. The stability of the disease free and endemic equilibriums is investigated for any time delay. Correspon- ding optimal control problems, with time delays in both state and control variables, are formulated and studied. In the second part, we propose a mathematical model for the transmission dynamics of human immunodeficiency virus (HIV).

Speakers:
P. G. Romeo
Date: Tuesday, 28 June, 2016
Abstract:

A crossconnections between two balanced categories $\mathcal{C}$ and $\mathcal{D}$ is a local isomorphism $\Gamma : \mathcal{D}\to B*\mathcal{C}$ where $B*\mathcal{C}$ is the balanced dual of $\mathcal{C}$ such that the image of $\Gamma$ is total in $B*\mathcal{C}$. It is also such a crossconnection $\Gamma$ determines a concordant semigroup.

Speakers:
A. R. Rajan
Date: Tuesday, 28 June, 2016
Abstract:

Categories have been frequently used as a convenient tool in describing the structure of regular semigroups. Inductive groupoids of Schein for inverse semigroups, inductive groupoids of KSS Nambooripad for regular semigroups, categories of Rees groupoids of AR Rajan, normal categories of KSS Nambooripad, etc., are some of the instances. In this talk we consider normal categories associated with different classes of regular semigroups. Further the subcategories of inclusions, isomorphisms and retractions in normal categories will also be discussed.

Speakers:
Alfonso Zamora
Date: Friday, 1 July, 2016
Abstract:

Given a reductive group G and an affine G-scheme X, constellations are G-equivariant sheaves over X such that their module of global sections has finite multiplicities. Prescribing these multiplicities by a function h, and imposing a stability condition $\theta$ there is a moduli space for $\theta$-stable constellations constructed by Becker and Terpereau, using Geometric Invariant Theory. This construction depends on a finite subset D of the set of irreducible representations of G.

Speakers:
Luis Álvarez-Cónsul
Date: Friday, 1 July, 2016
Abstract:

Y. Yang observed 20 years ago that the 2-sphere is the only compact orientable surface admitting solutions of the Einstein-Bogomol'nyi equations, coupling vortices with gravity, and obtained sufficient conditions for the existence of cosmic strings in this situation. In this talk, we will give an algebro-geometric interpretation of Yang's conditions, and explain why they are in fact necessary for the existence of solutions.

Speakers:
A. Okunev
Date: Friday, 17 June, 2016
Abstract:

An iterated function system (IFS) on a manifold M is a tuple of smooth maps f1, ...,fs : M → M. One of the reasons for studying IFS's is that they (more precisely, associated step skew products over Bernoulli shift) provide a nice model example of partially hyperbolic skew products. If some interesting robust property is found for the IFS's, it is often possible to find this property for a locally generic set of diffeomorphisms (see, e.g., [1]).

Speakers:
Luís Diogo
Date: Wednesday, 22 June, 2016
Abstract:

TBA

Speakers:
Artur de Araujo
Date: Tuesday, 28 June, 2016
Abstract:

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 defficiencies.

Speakers:
Fernando Lucatelli Nunes
Date: Tuesday, 28 June, 2016
Abstract:

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 theories” (or “homology theories”) which are examples of stable phenomena in homotopy theory. The concept of a prespectrum was first introduced by Elon Lages Lima in his PhD thesis to study some kinds of stable phenomena, such as Spanier-Whitehead duality and Stable Postnikov invariants.

Speakers:
Andrea Solotar
Date: Friday, 17 June, 2016
Abstract:

Let $K$ be a fixed field. Given parameters $(\alpha,\beta,\gamma) \in K^{3}$, the associated down-up algebra $A(\alpha,\beta,\gamma)$ is defined as the quotient of the free associative algebra $K\cl{u,d}$ by the ideal generated by the relations

\begin{split}
d^{2} u - (\alpha d u d + \beta u d^{2} + \gamma d),\\
d u^{2} - (\alpha u d u + \beta u^{2} d + \gamma u).
\end{split}

This family of algebras was introduced by G. Benkart and T. Roby.

Speakers:
Carlos Ramos
Date: Friday, 3 June, 2016
Abstract:

We discuss a simple model formed by two iterated maps of the interval, m and r: The map r, named regulatory map, controls the behavior of the map m, which is seen as an abstraction of the metabolism concept.