Geometry, Topology and Dynamics Seminar
Jenya Sapir
University of Illinois at Urbana-Champaign
Counting non-simple closed curves on surfaces
Abstract: We show how to get coarse bounds on the number of (non-simple) closed geodesics on a surface, given upper bounds on both length and self-intersection number. Recent work by Mirzakhani and by Rivin has produced asymptotics for the growth of the number of simple closed curves and curves with one self-intersection (respectively) with respect to length. However, no asymptotics, or even bounds, were previously known for other bounds on self-intersection number. Time permitting, we will discuss some applications of this result.
Monday October 19, 2015 at 3:00 PM in SEO 636