Billiards, dynamics, and the moduli space of Riemann surfacesLecture

by Paul Apisa

Tuesday Jan 13, 2026, 10:00 AM → 10:45 AM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

The Hodge bundle is the space whose points correspond to Riemann surfaces equipped with holomorphic 1-forms. This space admits a GL(2, R) action whose dynamics governs the geometry of the moduli space of Riemann surfaces, an object of central importance in geometry, algebra, and physics. Building on work of Eskin and Mirzakhani, I will describe my work on a program to classify GL(2, R) orbit closures and derive consequences for deceptively simple sounding problems about billiards in polygons. Along the way, I will describe an application of Hurwitz spaces to realize a hope of McMullen of describing intricate orbit closures with finite combinatorial data.