Geometry, Topology and Dynamics Seminar
Spencer Dowdall
Univ. of Illinois Urbana-Champaign
Statistical hyperbolicity in Teichmuller space
Abstract: The Teichmuller space of a closed surface exhibits many aspects of negative curvature but fails to be hyperbolic in any global sense. In this talk I will discuss the "statistical hyperbolicity" of Teichmuller space as reflected in the average distances between points in the ball or radius R and also the expected thinness of geodesic triangles. While the competing phenomena of negative and nonnegative curvature both influence these quantities, we will show that negative curvature wins out on average by studying the behavior of generic geodesic rays and establishing a thin triangle result in this setting. This is joint work with Moon Duchin and Howard Masur.
Monday April 28, 2014 at 3:00 PM in SEO 636