Geometric properties of Anosov representations- Guillaume Dreyer

Conference Title: GEAR Retreat 2012 Theme: Special Representations (3 of 5) Title: Geometric properties of Anosov representations Speaker: Guillaume Dreyer, Univ. of Souther California / Notre Dame; Date and Time: Monday August 6, 14:00 Description: In order to study the elements in the Hitchin space H(S), F. Labourie introduced the notion of Anosov representation. In particular, he proved that every Anosov representation is discrete and injective, some properties already shared by Teichmuller representations. The purpose of this talk is to extend to Anosov representations some classic tools from hyperbolic geometry designed to study Teichmuller representations: we generalize Thurston's length function and cataclysm deformation, and we analyse how they relate to each other. We shall then discuss how these techniques provide crucial information about a new system of coordinates on the Hitchin space H(S). Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: Guillaume Dreyer, in this GEAR Retreat 2012 session on Special Representations, will extend to Anosov representations some classic tools from hyperbolic geometry designed to study Teichmuller representations.