Academic Report of School of Mathematical Sciences [2026] No. 106

(Series Report for High-Level University Construction No. 1365)

Title：Short Course on Weil-Petersson Random Hyperbolic Surfaces

Speaker：Assistant Professor Xue Yuhao (Fudan University)

Time：Nov. 13-17, 2026 (See the course schedule below for specific details)

Location：Room 1420, Huiwen Building

Abstract:There exists a Riemannian metric of finite volume on the moduli space of hyperbolic surfaces, known as the Weil-Petersson metric. When normalized, this metric defines a probability measure on the moduli space, allowing us to discuss the concept of a stochastic hyperbolic surface. As the genus of the surface tends to infinity—unlike in the study of individual hyperbolic surfaces—many geometric properties of these random hyperbolic surfaces can be characterized with greater precision and exhibit highly regular statistical behavior. The new field of Weil-Petersson random hyperbolic surfaces began with some creative work by Mirzakhani about 20 years ago and has developed particularly rapidly in recent years. We will begin with hyperbolic surfaces and their moduli spaces, providing a detailed account of the foundations and developmental trajectory of this field. We will focus primarily on Mirzakhani’s related work and conclude by discussing the state of the field as of about five years ago.

Speaker Profile：Xue Yuhao is an assistant professor at Fudan University and the recipient of the 17th Zhong Jiaqing Mathematics Award. He earned his bachelor’s degree in 2018 and his Ph.D. in 2023 from Tsinghua University, and conducted postdoctoral research at the Institut des Hautes Études Scientifiques (IHES) in France from 2023 to 2026. His research focuses on Teichmüller theory, specifically the spectral and geometric properties of hyperbolic surfaces of high genus.

Class Schedule: November 13, 15, and 17, 2026, 9:00–11:00 a.m.

November 14 and 16, 2026, 2:30–4:30 p.m.

Invited by: Zhou Ze

School of Mathematical Sciences

October 30, 2026