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

Axel Grünrock, *University of Wuppertal*

```
```###
On well-posedness theory for nonlinear wave equations aside from the
${H}^{s}$-scale

The Cauchy problem for the cubic nonlinear Schrödinger equation $${\mathrm{iu}}_{t}+{u}_{\mathrm{xx}}=\mid u{\mid}^{2}u,\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}u(x\mathrm{,0})={u}_{0}(x)$$ is considered, with
emphasis on the case of one space dimension, i.e., $x\in R$. We
review the meanwhile classical results of Tsutsumi and
Cazenave/Weissler concerning data in the standard Sobolev spaces
${H}^{s}({R}^{n})$. Two invariance properties of the equation---scaling and
Galilean invariance---lead to certain obstructions to (time local)
well-posedness. A related counterexample of Kenig, Ponce, and Vega
showing ill-posedness is sketched. As a consequence, in the
one-dimensional case the restriction to ${H}^{s}(R)$-data seems to be
inadequate. A generalization of the standard theory due to the
author is presented. Finally, we discuss several other canonical
dispersive equations, such as KdV, mKdV, and DNLS, for which very
similar problems appear.

###
10/07/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

Denis Bonheure, *Université de Louvain-la-Neuve*

```
```###
Symmetry breaking in Moser-Trudinger inequalities and a Hénon type problem in dimension two

In this talk, we discuss a Hénon type functional with an exponential nonlinearity in dimension two. To study the symmetry properties of maximizers, we establish a link with Moser-Trudinger inequalities and consider the symmetry properties of the extremal functions for these inequalities.

###
28/06/2007, 11:00 — 12:00 — Room P3.10, Mathematics Building

Frédéric Paugam, *Institut de Mathématiques de Jussieu, Paris*

```
```###
A survey of the geometry of the functional equation of Riemann's zeta function

###
27/06/2007, 15:00 — 16:00 — Room P4.35, Mathematics Building

Frédéric Paugam, *Institut de Mathématiques de Jussieu, Paris*

```
```###
Noncommutative geometry and number theoretical dynamical systems

###
26/06/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

Benjamin Steinberg, *Carleton University, Canada*

```
```###
Spectral computations for self-similar groups

Self-similar groups, also known as automaton groups, have recently been popularized by the Grigorchuk school. They are groups acting on Cantor sets in such a way that their structure mimics the self-similarity of the Cantor set. Many interesting problems have been solved using self-similar groups including Milnor's problem on growth, Day's problem on elementary amenable groups, Hubbard's twisted rabbit problem, to name a few.

Grigorchuk and Zuk used a self-similar action of the lamplighter group to compute the spectral measure for the simple random walk with respect to its self-similar generating set. This led to a counterexample to the strong form of Atiyah's conjecture on ${L}_{2}$-betti numbers. Dicks and Schick generalized the result to wreath products $G$ wr $Z$ with $G$ a finite group and with "analogous" generators using a different technique. We recover Dicks and Schick's results using the original method of Grigorchuk and Zuk. In the process we clarify the relationship between the Kesten spectral measure and a spectral measure introduced by Grigorchuk and Zuk for self-similar groups. This is joint work with Mark Kambites and Pedro V. Silva.

###
19/06/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

Radoslaw Czaja, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

```
```###
Transversality in Scalar Reaction-Diffusion Equations on a Circle

We prove that stable and unstable manifolds of hyperbolic periodic orbits for general scalar reaction-diffusion equations on a circle \( u_t=u_{xx}+f(x,u,u_x),\ t\in\mathbb{R},\ x\in S^1, \) always intersect transversally. The argument also shows that for a periodic orbit there are no homoclinic connections. The main tool used in the proofs is Matano's zero number theory dealing with the Sturm nodal properties of the solutions.

###
12/06/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building

Alfonso Sorrentino, *Princeton University*

```
```###
On the total disconnectedness of the quotient Aubry set

In Mather's studies on the existence of Arnold diffusion, it turns
out that it might be useful to understand certain metric aspects of
what is called the quotient Aubry set. In particular, it seems to
be interesting to know whether this set has a "small" dimension. We
prove that under suitable hypotheses on the Lagrangian, the
associated quotient Aubry set, corresponding to a certain
cohomology class, is totally disconnected, i.e., every connected
component consists of a single point. We will also discuss the
relation between this problem and a Morse-Sard-like property for
(difference of) critical subsolutions of Hamilton-Jacobi equation.

###
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.