Aarhus University Seal / Aarhus Universitets segl

Seminar by Jenya Sapir (Univ. Illinois at Urbana Champaign)

Title: Counting non-simple closed curves on surfaces

2015.05.29 | Christine Dilling

Date Thu 11 Jun
Time 16:15 17:15
Location Physics aud. 1523-318

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.