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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
  • Moduli space

  • Weil-Petersson metrics

  • Deligne-Mumford compactification

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



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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