Group actions, warped cones and expanders

David Fisher (Indiana)

Abstract: The talk focuses on connections between basic questions is two areas of mathematics. The first is the classification of group actions up to conjugacy, a fundamental question in dynamics. The second is the classification of metric spaces up to quasi-isometry, a fundamental question in coarse geometry. Using John Roe's notion of a warped cone over a group action, we show that for a certain class of group actions/metric spaces, these questions are equivalent. I.e. from a group action one can construct a metric space which is a complete conjugacy invariant for a certain class of group actions. If time permits, I will also describe some applications to the coarse geometry of expanders and superexpanders and to the coarse Baum Connes conjecture.