Princeton University
Clay Mathematics Institute
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.