Mon, 07 Mar 2016
15:45
L6

Anosov representations and proper actions

Fanny Kassel
(University of Lille 1)
Abstract
 
Anosov representations of word hyperbolic groups into semisimple Lie groups provide a generalization of convex cocompact representations to higher real rank. I will explain how these representations can be used to construct properly discontinuous actions on homogeneous spaces. In certain cases, all properly discontinuous actions of quasi-isometrically embedded groups come from this construction. This is joint work with F. Guéritaud, O. Guichard, and A. Wienhard. 
Mon, 19 Oct 2015

16:00 - 17:00
Oxford-Man Institute

Computing harmonic measures for the Lévy stable process

THOMAS SIMON
(University of Lille 1)
Abstract

Abstract:In the first part of the talk, using classical hypergeometric identities, I will compute the harmonic measure of finite intervals and their complementaries for the Lévy stable process on the line. This gives a simple and unified proof of several results by Blumenthal-Getoor-Ray, Rogozin, and Kyprianou-Pardo-Watson. In the second part of the talk, I will consider the two-dimensional Markov process based on the stable Lévy process and its area process. I will give two explicit formulae for the harmonic measure of the split complex plane. These formulae allow to compute the persistence exponent of the stable area process, solving a problem raised by Zhan Shi. This is based on two joint works with Christophe Profeta.

 

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