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On the Growth of the Weil-Petersson Diameter of Moduli Space

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Will Cavendish (Princeton)

Abstract: The Weil-Petersson metric on Teichmuller space is a negatively
curved Kahler metric that relates in interesting ways to hyperbolic
geometry in dimensions 2 and 3. Though this metric is incomplete, its
completion is a CAT(0) metric space on which the mapping class group
acts cocompactly, and the quotient of this completion by the mapping
class group is the Deligne-Mumford compactification of moduli space
M_{g,n}. I will give a brief introduction to
Weil-Petersson geometry and discuss joint work with Hugo Parlier that
studies the growth of
diam(M_{g,n}) as g and n tend to
infinity.