Anders Karlsson: Dynamics on Teichmüller spaces

Questions about the dynamics of holomorphic maps or mapping class elements on Teichmüller spaces arise for example in Thurston´s theories on 3-manifolds, the classification of surface diffeomorphims and the combinatorics of rational maps. I'll describe some recent results on this topic, for example that given a holomorphic self-map there is an extremal length which does not increase under iteration and statements on random products of mapping class elements which can be viewed as extensions of the Nielsen-Thurston classification of surface diffeomorphisms or as nonlinear analogs of the multiplicative ergodic theorem for matrices.  I'll begin by recalling the relevant basics about Teichmüller spaces and mapping class groups.