Abstract

I will present some recent results on rigidity of group actions and flows that come from looking at induced actions on “boundaries at infinity”. This idea has a long history, going back to Selberg and Mostow. In some of my recent joint work, I use this approach in geometric group theory and dynamics, studying boundary rigidity for actions of hyperbolic groups on their Gromov boundary, and showing Anosov flows on 3-manifolds are determined by their periodic orbits. This talk will survey some of the history, philosophy and techniques related to proving rigidity results by looking out to infinity.