The Weil-Petersson metric on the moduli space of genus $g$ hyperbolic surfaces is of finite volume, and hence induce a probability measure and a model of random surfaces. In this talk, we will discuss about the behavior of several different types of closed geodesics on Weil-Petersson random hyperbolic surfaces, and see in which length window they should exist . In particularly, we will show the length of separating systole and non-simple systole on Weil-Petersson random hyperbolic surfaces. This talk is based on a series of joint works with Yuxin He, Xin Nie, Yang Shen and Yunhui Wu.

Speaker Biography: Yuhao Xue is currently a postdoctoral researcher at the Institut des Hautes Études Scientifiques (IHES) in France. He received his Bachelor's degree in 2018 and his Ph.D. in 2023, both from Tsinghua University. His primary research area is Teichmüller theory, with a particular focus on the behavior of various geometric quantities on hyperbolic surfaces.