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.

报告人简介：薛宇皓现为法国高等科学研究所(IHES)博士后，2018年和2023年于清华大学分别获得学士和博士学位。主要研究领域为Teichmüller理论，特别地，研究双曲曲面上各种几何量的行为。