Department of Mathematics

Princeton University

Clay Mathematics Institute

Tuesday, September 20

4 PM - 5 PM Herman Brown 227

Wednesday, September 21

4 PM - 5 PM Herman Brown 227

Friday, September 23

4 PM - 5 PM Herman Brown 227

In this lecture series, we discuss the relationship between simple geodesics o hyperbolic surfaces and the Weil-Petersson geometry of the moduli space of curves. We give a recursive method for calculating Weil-Petersson volume of the moduli space of bordered Riemann surfaces. Also, we study the growth of the number of simple closed geodesics on hyperbolic surfaces. Finally, we obtain a new proof of the Witten-Kontsevich formula for the intersection numbers of tautological classes on the moduli space of curves.

There will be a tea preceding each lecture at 3:30PM in the Mathematics Commons Room, Herman Brown 438.

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