Talk page

Title:
The moduli space of Riemann surfaces and the Weil-Petersson metric

Speaker:
Xuwen Zhu

Abstract:
The subject of this talk is the moduli space of Riemann surfaces, which is the set of isometry classes of constant curvature metrics on a surface. The cotangent space of the moduli space is given by holomorphic quadratic differentials, and there is a natural Weil-Petersson metric defined by an $L^2$-type pairing. I will discuss the behavior of the moduli space when approaching the boundary of the Deligne-Mumford compactification, and show how to use tools from microlocal analysis to understand the degeneration of the Weil-Petersson metric.

Link:
https://www.msri.org/workshops/894/schedules/27295

Workshop:
MSRI- Connections for Women: Holomorphic Differentials in Mathematics and Physics