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Analysis, Geometry, and Dynamical Systems Seminar   RSS

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

Attractors for Semilinear Parabolic Equations on the Circle

27/07/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building
, 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
, Universidade de São Paulo

Discretization of Unidimensional Functional Partial Equations

06/07/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building
, 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 [X] is multiplicity free as a G -module. Knop's conjecture states that if moreover X is smooth, the module structure of C [X] 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
, Instituto Superior Técnico

Stability of nonautonomous differential equations

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