Title: Asymptotic geometry of the mapping class group and Teichmuller space
Jason Behrstock (Columbia University)
Tuesday, September 28 at 1:30pm in Malott 406
Abstract:
I will discuss some recent progress towards understanding the asymptotic
geometry of mapping class groups. Using techniques involving the complex
of curves, the first part of my talk will explain some properties of maps
from the mapping class group to the curve complex of a subsurface X, which
are closely related to the map taking a curve in S to its intersection
with X. The second half will describe how the geometry of the mapping
class group is encoded by these maps; here we will discuss the
relationship between these "projection" maps and the topology of the
asymptotic cone of the mapping class group. I will also relate this to a
discussion of Teichmuller space with the Weil-Petersson metric; in
particular I will discuss a new proof of the hyperbolicity of Teich in
the low genus cases.