The birthday problem for random surfaces

Jenya Sapir (Binghamton)

Abstract: There has been quite a bit of interest in recent years in the geometry of random hyperbolic surfaces of high genus. It turns out there are strong parallels between the theory of random surfaces and the theory of random regular graphs. In this talk, I will discuss recent joint work with Ben Dozier, where we prove counting results for closed geodesics in both settings. In particular, I will discuss how the count for simple closed geodesics in both graphs and surfaces is related to the famous birthday problem in probability.