### 06/06/2007, 11:00 — 12:00 — Room P3.10, Mathematics Building

Marius Dadarlat, *Purdue University*

### Bundles, Operator Algebras and $K$-theory

The bundles that occur naturally in functional analysis are not
necessarily locally trivial. Dixmier and Douady have shown that a
continuous bundle with fiber an infinite dimensional separable
Hilbert space $H$ over a compact contractible metric space does not
need to be trivial, even though the unitary group of $H$ is
contractible. Similar phenomena appear in the theory of operator
algebras. The operator algebras with Hausdorff primitive spectrum
are known to be isomorphic to algebras of sections in certain
continuous bundles which are typically not locally trivial. We plan
to give a gentle introduction illustrated by examples to the
$K$-theory methods used in the study of these bundles.

### 05/06/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

Alex Kumjian, *University of Nevada, Reno*

### On Hausdorff Measures and KMS States

We explore an intriguing correspondence between Hausdorff measures
arising from self-similar metrics and KMS states. This
correspondence identifies the Hausdorff dimension of the space with
the inverse temperature of the KMS state.
This talk is partially based on joint work with Jean
Renault.

### 17/05/2007, 11:00 — 12:00 — Room P3.10, Mathematics Building

Rachid El Harti, *University Hassan I, Morocco*

### Operator Algebras and Amenability

### 24/04/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

Emma D'Aniello, *Seconda Universitá degli Studi di Napoli*

### Chaos, periodic orbits and
$\omega $-limit sets

### 06/03/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

Messoud Efendiev, *Technische Universität München*

### On a new class of equations arising in the modelling of biofilms

### 23/02/2007, 11:00 — 12:00 — Room P3.10, Mathematics Building

Jacob Palis, *IMPA, Rio de Janeiro*

### A Global Scenario for Chaotic Systems from Poincaré to Present Time

In simple and reasonably nontechnical language, I shall discuss
Poincaré's viewpoint that a key question in dynamics was to
describe for most systems their global orbit structure. Poincaré
suggested the question more than one hundred years ago and it is
still a major question in the area. I will include in the
discussion the important topic of homoclinic bifurcations, which
curiously played a dramatic role in Poincaré's essay that led him
to receive a prize from King Oscar II of Sweden.

### 13/02/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

David Iglesias Ponte, *Instituto de Matemáticas y Física Fundamental, CSIC-Madrid*

### New geometric techniques in mechanics

We will develop a geometric description of Lagrangian Mechanics on
Lie algebroids (generalizing Klein's formalism on the tangent
bundle). The main motivation comes from reduction theory of
Lagrangian systems. If time permits we will explain how Lie
groupoids appear in discrete mechanics and the relation between
both theories.

### 08/02/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

Gonzalo Contreras, *CIMAT, México*

### A generic property of families of Lagrangian systems

We prove that a generic Lagrangian has finitely many minimizing
measures in all the cohomology classes. In particular, for a
generic Lagrangian, the quotient Aubry set is finite for all
cohomology classes.

### 30/01/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

Artur Lopes, *Universidade Federal do Rio Grande do Sul, Brazil*

### Holonomic Probabilities and Ergodic Optimization

### 23/01/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jan Cholewa, *University of Silesia, Katowice, Polónia*

### Dissipative equations in locally uniform spaces

Semilinear damped wave equations, partly dissipative systems and reaction diffusion equations in ${\mathbb{R}}^{N}$ are considered in the locally uniform spaces under the assumptions on the nonlinear term similar to those in bounded domains.

### 07/12/2006, 14:00 — 15:00 — Room P4.35, Mathematics Building

Peter Raith, *Universität Wien*

### Continuity properties of pressure and entropy for piecewise
monotone interval maps

### 05/12/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Andrey Biryuk, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### Analysis of a pressureless dynamical system and an open geometrical
problem

We consider the pressureless Euler equation equipped with periodic
boundary conditions. The criterion for the global smooth
solvability can be given in terms of degeneracy of the initial
state: the Jacoby Matrix must be everywhere nilpotent. A simple
purely geometrical reformulation of the above condition is possible
in the 2D case. The question is open for higher dimensions. An
application to turbulence is also discussed.

### 29/11/2006, 15:00 — 16:00 — Room P4.35, Mathematics Building

Francisco Balibrea, *Universidade de Murcia*

### Geometric unfolding of some difference equations

### 29/11/2006, 14:00 — 15:00 — Room P4.35, Mathematics Building

Antonio Linero, *Universidade de Murcia*

### Some results on omega-limit sets of two-dimensional permuted direct
product maps

### 29/11/2006, 11:30 — 12:30 — Room P4.35, Mathematics Building

Irina Sushko, *Academia das Ciências de Kiev*

### Bifurcation structure of parameter plane for a family of unimodal
piecewise smooth maps: border-collision bifurcation curves

### 28/11/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Alexandre Carvalho, *Universidade de São Paulo, São Carlos*

### Strongly damped wave equations: Continuity of attractors

### 21/11/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jaume Llibre, *Universitat Autònoma de Barcelona*

### The set of periods for the Morse-Smale diffeomorphisms on
${T}^{2}$

We shall use the Lefschetz zeta function for studying the set
of periods of the Morse-Smale diffeomorfisms defined on the
2-dimensional torus for every homotopy class.

### 15/11/2006, 15:00 — 16:00 — Room P4.35, Mathematics Building

Ruy Exel, *Universidade Federal de Santa Catarina*

### Algebras associated to irreversible dynamical systems

### 31/10/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

Arnaldo Nogueira, *Institut de Mathématiques de Luminy*

### Ergodic properties of triangular partitions

### 24/10/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building

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

### Phase transitions and multifractal analysis for horseshoes.