What does a random surface look like?

What does a random surface look like?

Speaker：

Kasra Rafi (University of Toronto)

Time：

Wed., 16:00-17:00, Nov. 19, 2025

Venue：

C548, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 271 534 5558

Passcode: YMSC

Abstract:

Building on her seminal work on moduli space volumes for Riemann surfaces, Mirzakhani also computed expected values of various geometric quantities on moduli space. In particular, she studied the expected Cheeger constant, the injectivity radius at a random point, and the statistical distribution of different types of curves on surfaces of large genus. I will review several of Mirzakhani’s key results, which together give a detailed picture of the geometry of random high genus surfaces. I will then discuss some extensions of her work in the setting of translation surfaces.