III: Counting mapping class group orbits on hyperbolic surfaces

Minerva Lectures at Princeton University
Topic:III: Counting mapping class group orbits on hyperbolic surfaces
Speaker:Maryam Mirzakhani
Affiliation:Stanford University; Member, School of Mathematics
Date:Friday, November 13
Time/Room:4:30pm - 5:30pm/McDonnell A02, Princeton University

Let $X$ be a complete hyperbolic metric on a surface of genus $g$ with $n$ punctures. In this lecture I will discuss the problem of the growth of $s^{k}_{X}(L)$, the number of closed curves of length at most $L$ on $X$ with at most $k$ self-intersections. More generally, we investigate the properties of the orbit of an arbitrary closed curve $\gamma$ under the action of the mapping class group. I will also discuss problems regarding the distribution of the corresponding geodesics on $T^1(X)$.