Speaker: Keith Burns (Northwestern)
Title: Mixing properties of the Weil-Petersson geodesic flow
Abstract: I will talk about the geodesic flow for the Weil-Petersson metric on the moduli space of a surface that supports hyperbolic metrics. This is a Riemannian metric with negative sectional curvatures. However the classical results of Anosov do not apply because the metric is incomplete and the sectional curvatures and their derivatives are not uniformly bounded. It was not until the 21st century that this geodesic flow was shown to be mixing (and in fact Bernoulli).
I will give some ideas from the proof and also from more recent work directed towards showing that the flow is exponentially mixing in case of the torus with one puncture.
This is joint work with Howie Masur, Carlos Matheus, and Amie Wilkinson