Geometry and Topology Seminar: Counting double cosets in groups with contracting elements

Speaker: Suzhen Han from Hunan University

Organizer: Xiaolong Han

Abstract: There are numerous groups with contracting elements, where counting problems are systematically studied by Yang and others. In particular, we will discuss in this talk the growth of double cosets in groups with contracting elements.

As an application, we consider the mapping class group acts on the Teichmuller space with Teichmuller metric, and we establish a geometric complexity on the 3-manifolds with a Heegaard splitting of fixed genus by studying an orbit of the mapping class group. We show that generic 3-manifolds are hyperbolic with respect to the geometric complexity. This is a joint work with Wenyuan Yang and Yanqing Zou.

Time: 04/16, 2:30-3:30pm, 4/17, 9:30-10:30 am.

Location: Online
Zoom Meeting ID: 974 6773 9421 (Passcode: 698778)