### 22/02/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building

Tobias Weth, *Universität Giessen*

### Partial symmetry of solutions to some variational problems

We study symmetry properties of several radially symmetric
minimization problems. The minimizers which we obtain are sign
changing solutions of superlinear elliptic problems or
eigenfunctions of weighted asymmetric eigenvalue problems. In both
instances we prove that the minimizers have a foliated Schwarz
symmetry, but in general they are not radially symmetric. The basic
tool which we use is polarization, a two point rearrangement which
is useful especially for the study of symmetry properties of sign
changing functions. This is joint work with T. Bartsch and
M. Willem.

### 25/01/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building

Mahendra Panthee, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### Global solutions for the modified KdV equation

### 18/01/2005, 15:00 — 16:00 — Room P3.10, Mathematics Building

Tiago Domingos, *Instituto Superior Técnico*

### The Formal Unification of Thermodynamics and Microeconomics

### 14/12/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Philippe Gimenez, *Universidad de Valladolid*

### Sparse changes of coordinates for computing the Castelnuovo-Mumford regularity

Let $I$ be a homogeneous ideal of $R$, the polynomial ring in $n+1$ variables over an arbitrary field $K$. The Castelnuovo-Mumford regularity of $I$ is a numerical invariant related, on one hand, to the minimal graded free resolution of $I$, and on the other to the graded cohomology modules of $R/I$. In this work, avoiding the construction of a minimal graded free resolution of $I$, we provide effective methods for computing the Castelnuovo-Mumford regularity of $I$ that also compute other cohomological invariants of $R/I$. We do this following the philosophy of Bayer and Stillman in their celebrated paper (Inventiones, 1987) making changes of coordinates. The problem with generic projective changes of coordinates is that they usually destroy the sparsity of the ideal and hence are not useful from the computational point of view. In this work, the changes of coordinates we make depend on the ideal $I$ and take advantage of some properties of the ideal. In the worst case, the changes of coordinates are sparse enough to be used for computing the regularity. We will give several examples where the regularity is obtained in a few seconds using our methods while a minimal graded free resolution could not be obtained. When the field K is infinite, we also obtain for free a new algorithm for computing a Noether normalization of $R/I$ that provides a significant improvement of the methods known until now. This is joint work with Isabel Bermejo (University of La Laguna, Spain). The results presented in this talk have been implemented in the package SINGULAR 2.0.5 (http://www.singular.uni-kl.de/) in a specific distributed library co-written with Gert-Martin Greuel (University of Kaiserslautern, Germany).

### 30/11/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

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

### Multifractal analysis for countable Markov shifts

### 25/11/2004, 11:00 — 12:00 — Room P3.10, Mathematics Building

Saber Elaydi, *Trinity University, San Antonio*

### Global stability in autonomous and nonautonomous discrete dynamical
systems II

### 23/11/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Saber Elaydi, *Trinity University, San Antonio*

### Global stability in autonomous and nonautonomous discrete dynamical
systems I

### 16/11/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Pedro Silva Santos, *Instituto Superior Técnico*

### $A$-quasi-convexity

### 09/11/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Rémi Carles, *Université Bordeaux I e Centro de Matemática e Aplicações
Fundamentais*

### Schrödinger equations with potential and hyperbolic Hamiltonian

### 26/10/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

David Lannes, *Université Bordeaux I*

### Well-Posedness of the Water-Waves Equations

The water-waves problem consists in finding the motion of the free
surface of a perfect, incompressible and irrotational fluid under
the influence of gravity. Such a motion is described by the Euler
Equations with free surface. I will propose a proof of the
well-posedness of these equations, which is quite elementary. I
will comment on various of the tools involved in the proof:
Dirichlet-to-Neuman operators, regularizing diffeomorphisms, shape
optimization, Nash-Moser iterative scheme, etc.

### 19/10/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Jeroen Lamb, *Imperial College, London*

### The geometry of Penrose tilings: projection and substitution

In the early 1970's, R. Penrose constructed a set of two tiles that
can tile the plane only nonperiodically. His proof uses a
renormalization argument based on the existence of substitution
rules. In 1981, N. de Bruijn showed that Penrose tiling also can be
obtained by projection of a discrete plane in ${R}^{5}$ (with vertices
in ${Z}^{5}$) to the nearest two-dimensional hyperplane. In this talk
we show that projection tilings of this type admit (a countable
infinity of different) substitution rules if and only if there
exists a "quadratic" (partially) hyperbolic lattice automorphism
that commutes with the projection. As the latter condition is very
easy to verify, we obtain a simple characterization (and many new
examples) of such renormalizable projection tilings. This is joint
work with Edmund Harriss.

### 12/10/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Katrin Gelfert, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### Multifractal analysis for Lyapunov exponents

### 28/09/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Carlos Rocha, *Instituto Superior Técnico*

### Attractors for Semilinear Parabolic Equations on the Circle

### 27/07/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Irene Fonseca, *Carnegie Mellon University, Pittsburgh*

### Second order variational problems

### 20/07/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Giovanni Leoni, *Carnegie Mellon University, Pittsburgh*

### Optimal regularity for free boundary problems and a conjecture of
De Giorgi

### 08/07/2004, 11:00 — 12:00 — Room P3.10, Mathematics Building

Sérgio Oliva, *Universidade de São Paulo*

### Discretization of Unidimensional Functional Partial Equations

### 06/07/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Bart Van Steirteghem, *Columbia University*

### A classification of affine smooth spherical varieties

F. Knop has translated Delzant's conjecture (1990) on compact
multiplicity free spaces (also known as noncommutative completely
integrable systems) into a conjecture on affine smooth spherical
varieties. If $G$ is a reductive algebraic group (over $C$) and $X$
is an affine $G$-variety (over $C$), then $X$ is called spherical
if its coordinate ring $C\left[X\right]$ is multiplicity free as a $G$-module.
Knop's conjecture states that if moreover $X$ is smooth, the module
structure of $C\left[X\right]$ determines the $G$-variety $X$ up to
isomorphism. As a first step towards proving the conjecture, we
have classified these varieties, "up to pesky tori and connected
components".

### 29/06/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Pierre Martinetti, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### Renormalization and Hopf algebras

### 22/06/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Philippe Monnier, *Centro de Análise Matemática, Geometria e Sistemas Dinâmicos*

### A cohomology associated to a function

### 15/06/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building

Luis Barreira, *Instituto Superior Técnico*

### Stability of nonautonomous differential equations