Maryam Mirzakhani

Simple geodesics on hyperbolic surfaces and the Witten-Kontsevich formula

In this talk we discuss an algorithm for calculating the Weil-Petersson volume V_{g,n}(l) of the moduli space M_{g,n}(l) of bordered Riemann surfaces with fixed boundary lengths l_1,...,l_n. We show V_{g,n}(l) is a polynomial in l. We also relate the coefficients of V_{g,n}(l) to the intersection numbers of tautological classes on \bar{M}_{g,n}.