Convidamos a todos para a primeira palestra do Seminário de Geometria & Topologia do semestre 2016-1, quarta-feira proxima semana, dia 06/04:
Given a Lie group, the classical Van Est theorem relates global cohomological data on the Lie group (e.g. cohomology with values in some representation) with infinitesimal information depending only on its Lie algebra. Later, this theorem was generalized by Weinstein-Xu (for low degrees) and Crainic (for arbitrary degrees) to Lie groupoids providing a framework to study characteristic classes for Lie groupoids, obstructions to integrability among other things. In this talk, we shall study a special class of Lie groupoids and show how the Van Est theorem can be used to obtain a result relating representations up to homotopy of Lie groupoids and Lie algebroids.
Palestrante: Thiago Linhares Drummond (UFRJ)
In this talk we discuss the well-posedness issues of the associated initial value problem, the existence of nontrivial solutions with prescribed L^2 -norm, and the stability of associated solitary waves for two classes of coupled nonlinear dispersive equations. The first model describes the nonlinear interaction between two Schrödinger type short waves and a generalized Korteweg-de Vries type long wave and the second one describes the nonlinear interaction of two generalized Korteweg-de Vries type long waves with a common Schrödinger type short wave. The results here extend many of the previously obtained results for two-component coupled Schrödinger-Korteweg-de Vries systems.
This is a joint work with Adan Corcho and Santosh Bhattarai
Palestrante: Mahendra Panthee (Unicamp)
Data: 16/03/2016 (quarta feira)
Hora: 13:30 h
Resumo: We will deal with a 1-dimensional reaction-diffusion-convection PDE where the diffusion is of mean-curvature type and both convection and reaction terms are present. We will assume f(0) = 0 = f(1) and search for traveling-wave type solutions u(x; t) = v(x+ct) connecting the two equilibria 0 and 1.
Through the use of a suitable change of variables, we will translate this problem into the search for a solution to a two-point problem in the interval [0; 1], and determine the set of the admissible speeds (i.e., the numbers c for which a solution of this kind exists) for different kinds of reaction and convection terms, thanks to a shooting technique. We will also make some comments about the dependence of such admissible speeds on a viscosity parameter braking the diffusion.
Expositor: Maurizio Garrione
Local: Sala C116