### 17/10/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

José Maria Gomes, *Centro de Matemática e Aplicações Fundamentais*

### ${2}^{n}-1$ positive solutions to a superlinear elliptic problem with sign changing weight

### 03/10/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Dmitry Matsnev, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### The Baum-Connes conjecture and linear group actions on spaces of finite asymptotic dimension

The Baum-Connes conjecture describes the $K$-theory of a reduced crossed product of a ${C}^{*}$-algebra by a group $G$ in terms of the $K$-homology of the classifying space of proper actions of $G$. We shall describe the Conjecture for discrete group case and its connotations. Commenting on results of Guentner, Higson, Kasparov, Weinberger, and Yu, we investigate the possibility of applying a finite-dimensionality argument in order to prove parts of the Conjecture for discrete linear groups.

### 19/09/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Nuno Luzia, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### Measure of full dimension for nonconformal dynamics

### 12/09/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Messoud Efendiev, *Technische Universität München*

### On some class of nonautonomous equations and their attractors.

### 11/09/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Frank Morgan, *Williams College, Williamstown*

### The Double Bubble Theorem

### 16/06/2006, 11:00 — 12:00 — Room P3.10, Mathematics Building

Saber Elaydi, *Trinity University, San Antonio*

### From periodic to almost periodic dynamical systems

### 14/06/2006, 14:00 — 15:00 — Room P3.10, Mathematics Building

Saber Elaydi, *Trinity University, San Antonio*

### Topological properties of global atractors.

### 16/05/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Nuno Luzia, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### Hausdorff dimension for an open class of repellers in
${\mathbb{R}}^{2}$

We compute the Hausdorff dimension for an open class of *
Iterated Function Schemes* in ${\mathbb{R}}^{2}$ in the ${C}^{2}$
topology, in terms of the *pressure function*. This class is
characterized by a *domination condition* that is *not
too strong*, plus the *non-overlapping condition*. Also
in this class there exists a unique invariant probability measure
of full Hausdorff dimension. Finally we show that the Hausdorff
dimension is a continuous function in this class.

### 28/03/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Matthias Wolfrum, *Weierstrass Institute for Applied Analysis and Stochastics, Berlin*

### Systems of Delay Differential Equations with Large Delay

### 07/03/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Godofredo Iommi, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### Suspension flows over countable Markov shifts

### 21/02/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Gabriela Gomes, *Instituto Gulbenkian de Ciência*

### Fundamental assumptions in models of reinfection

### 14/02/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Pantelis Damianou, *University of Cyprus*

### The modular class and integrable systems

### 07/02/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Maria João Oliveira, *Universidade Aberta*

### Bogoliubov functionals: from measure theory to functional analysis

### 18/01/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Constantine Dafermos, *Brown University*

### Hyperbolic Conservation Laws with Contingent Entropies and
Involutions

### 13/12/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building

Roman Hric, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### Topology of minimal systems

I will start with a short survey of basic facts about minimal sets
and I will briefly discuss their role in the theory of dynamical
systems. In the second part, I will present recent results obtained
with F. Balibrea, T. Downarowicz, L. Snoha and
V. Spitalsky.

### 06/12/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building

Michal Málek, *Silesian University, Opava*

### Basic sets and distributional chaos in dimension one

The notion of basic set was introduced by A. N. Sharkovskii in the series of his papers from late sixties. These papers focused on omega-limit sets of continuous maps of the compact interval. It turned out later that existence of basic sets for a dynamical system on the compact interval corresponds to nontrivial behavior of the dynamical system: positive topological entropy, existence of horseshoes, distributional (and other) chaos.

In this talk we present results showing that similar behavior remains true when other one-dimensional spaces are considered (the circle, trees, graphs).

### 29/11/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building

João Martins, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### $2$-dimensional homotopy invariants of complements of embedded
surfaces in ${S}^{4}$

### 15/11/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building

Nuno Luzia, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### On Hausdorff dimension in higher dimensions

### 03/11/2005, 11:00 — 12:00 — Room P3.10, Mathematics Building

Arnaldo Mandel, *IME, Universidade de São Paulo*

### Faithful linear representions of the free group

Many families of matrices that generate free groups are known, notably constructions by Hausdorff (1907) and Sanov (1947). Topological arguments show that those families are ubiquitous, and Tits' Theorem of Alternatives (1972) gives deep algebraic reasons for that. On the other hand, faced with a pair of matrices, it is almost hopeless to decide whether they generate a free group. I will describe some that is known on explicit presentation of matrix generators of free groups, concentrating on joint work with Jairo Gonçalves and Mazi Shirvani, that describe explicit free groups in the multiplicative group of some finite dimensional algebras.

### 28/10/2005, 15:00 — 16:00 — Room P3.31, Mathematics Building

Tomasz Downarowicz, *Wroclaw University of Technology*

### Minimal realizations of Jewett-Krieger type for nonuniquely ergodic
systems II

In a topological dynamical system
$(X,T)$ the set of invariant measures is a Choquet simplex
$K(X,T)$ whose extreme points are ergodic measures. We will prove that for any zero-dimensional system
$(X,T)$ having no periodic points there exists a minimal system
$(Y,S)$ and an affine homeomorphism
$f$ between the Choquet simplexes
$K(X,T)$ and
$K(Y,S)$ such that for each
$m$ in
$K(X,T)$ the measure-theoretic systems
$(X,m,T)$ and
$(Y,f(m),S)$ are isomorphic. In this sense
$(Y,S)$ is a minimal model for
$(X,T)$. As an application we will derive the existence of minimal models with a preset collection of invariant measures (arranged in form of a simplex).