Geometry, Topology and Dynamics Seminar
Howard Masur
University of Chicago
Ergodicity of the Weil-Petersson geodesic flow
Abstract: This is joint work with Keith Burns and Amie Wilkinson.
Let $\Sigma$ be a surface of genus $g$ with $n$ punctures. We assume $3g-3+n>0$.
Associated to $\Sigma$ is the Teichmüller space. This is the space of hyperbolic metrics one can put on $\Sigma$, up to isotopy. The mapping class group acts on the Teichmüller space with quotient, the Riemann moduli space $\mathcal{M}(\Sigma)$. There are a number of interesting metrics on $\mathcal{M}(\Sigma)$; one of which is the Weil-Petersson metric. It is a Riemannian metric of negative curvature and finite volume but it is not complete.
In this talk I will discuss the background on this metric and the following theorem.
Theorem: The Weil-Petersson geodesic flow is ergodic on $\mathcal{M}(\Sigma)$.
Monday April 11, 2011 at 3:00 PM in SEO 636