Geometry, Topology and Dynamics Seminar
Howard Masur
UIC
The geometry of moduli space and the Deligne Mumford compactification
Abstract: Let S be a surface of genus g with n punctures. Associated to S is the moduli
space M_{g,n} of all conformal structures on S. Equivalently, this is the
space of hyperbolic metrics on S and also the space of algebraic curves. The
moduli space comes equipped with the Teichmuller metric. I will discuss some
properties of geodesic rays in this metric. Also associated to M_{g,n} is its
Deligne Mumford compactification found by adding Riemann surfaces with nodes.
I will discuss how one can recover the compactification purely from the study
of rays in the space. This is joint work with Benson Farb.
Monday September 17, 2007 at 3:00 PM in SEO 512