Abstract

In this talk, we will discuss the behavior of the separating systole for random hyperbolic surfaces with respect to the Weil-Petersson measure of the moduli space. We show that its length is approximately 2log(g)-4log(log(g)) and it separates out a one-holed torus for generic surfaces. Some other geometric quantities are also considered. This talk is based on joint works with Xin Nie, Hugo Parlier and Yunhui Wu.