Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Hyperbolic groups are generalizations of finitely generated free groups and surface groups, and they act properly and cocompactly by isometries on Gromov hyperbolic spaces. For a fixed hyperbolic group, we can pack all of its actions of this type into a single space, which extends the classically studied Teichmüller and Outer spaces, but contains many more interesting actions. I will talk about this space and some of its properties when it is equipped with a natural metric that resembles Thurston's Lipschitz distance on Teichmüller space. In particular, I will explain how to find many bi-infinite geodesics in this space, which I showed in joint work with Stephen Cantrell.