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 $T^1(X)$.