Title: The space of metrics on a hyperbolic group, Sullivan's measure, and rough symmetries.
Speaker: Alex Furman
Speaker Info: University of Illinois, Chicago
Many concepts associated to the geometry and dynamics of a negatively curved closed manifold, such as, topological entropy, lengths of closed geodesics, Sullivan's measure on the space of geodesics, admit a generalization to the framework of proper left invariant metrics on a Gromov hyperbolic group, taken up to bounded distance. This broader framework includes such objects as word metrics, and distances coming from convex cocompact actions of CAT(0) spaces. We shall overview this broader framework and show how one might single out fundamental groups of locally symmetric spaces and the locally symmetric metrics, among all other examples.Date: Sunday, October 31, 2010