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Nodal degeneration of hyperbolic metrics and application to Weil-Petersson metric on the moduli space

Presented by: 
X Zhu Massachusetts Institute of Technology
Date: 
Tuesday 28th July 2015 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
This is joint work with Richard Melrose. We analyze the behavior of the Laplacian on the fibres of a Lefschetz fibration and use it to describe the behavior of the constant curvature metric on a Riemann surface of genus $>1$ undergoing nodal degeneration. We apply this to deduce the asymptotics of the Weil-Petersson metric on the moduli space $\mathcal{M}_g$.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons