10/14/2004

Maryam Mirzakhani
Princeton University

Counting simple closed geodesics on hyperbolic
surfaces and McShane identities

In this talk we show that the number of simple closed geodesics of length at most L on a hyperbolic surface X of genus g has the asymptotic behavior

                            6g-6
              s (L) ~  n   L
               X        X

we will also discuss the problem of the frequencies of different types of simple closed geodesics on hyperbolic surfaces and show that relative frequencies are universal rational numbers independent of X.