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

## Connections for Women: Holomorphic Differentials in Mathematics and Physics August 15, 2019 - August 16, 2019

August 15, 2019 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Xuwen Zhu (Northeastern University)
Location: MSRI: Simons Auditorium
Tags/Keywords
• Moduli space

• Deligne-Mumford compactification

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

#### 03-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.

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