Mirzakharni's recursion formula is equivalent to the Witten-Kontsevich theorem

Abstract

In this paper, we give a proof of Mirzakhani's recursion formula of Weil-Petersson volumes of moduli spaces of curves using the Witten-Kontsevich theorem. We also describe properties of intersections numbers involving higher degree $\kappa$ classes.

13 pages, to appear in Asterisque

References in corpus (4)

• An algebro-geometric proof of Witten's conjecture
• Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models
• Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy
• A simple proof of Witten conjecture through localization

Cited by in corpus (4)

• Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
• Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes
• Towards large genus asymtotics of intersection numbers on moduli spaces of curves
• The Hodge-FVH Correspondence