Mirzakhani's recursion formula on Weil-Petersson volume and applications

Abstract

We give an overview of the proof for Mirzakhani's volume recursion for the Weil-Petersson volumes of the moduli spaces of genus $g$ hyperbolic surfaces with $n$ labeled geodesic boundary components, and her application of this recursion to Witten's conjecture and the study of simple geodesic length spectrum growth rates.

To appear in the Handbook of Teichmüller theory. 34 pages, 7 figures

References in corpus (1)

• An algebro-geometric proof of Witten's conjecture