Brandeis-Harvard-MIT-Northeastern Joint Mathematics Colloquium

Speaker: Simion Filip (University of Chicago) Title: Measure and topological rigidity beyond homogeneous dynamics Abstract: To study the asymptotic behavior of orbits of a dynamical system, one can look at orbit closures or invariant measures. When the underlying system has a homogeneous structure, usually coming from a Lie group, with appropriate assumptions a wide range of rigidity theorems show that ergodic invariant measures and orbit closures have to be well-behaved and can often be classified. I will describe joint work with Brown, Eskin, and Rodriguez Hertz, which establishes rigidity results for quite general dynamical systems with some hyperbolicity. I will discuss in detail a case with rich geometric structures, namely that of the action of the mapping class group and its subgroups on the character variety of a compact Lie group. Orbit closures in this case are related to the geometry of families of Riemann surfaces.