Visions in Arithmetic and Beyond: Celebrating Peter Sarnak's Work and Impact

Billiards and the Arithmetic of Non-Arithmetic Groups

Abstract: What are the slopes of periodic billiard paths in a regular polygon?

We will connect this question and others to:

        - cusps of thin groups,

        - curves on Hilbert modular varieties,

        - heights from Jacobians with real multiplication, and 

        - a spectral gap for the Galois orbits of triangles.

Along the way we will encounter issues of chaos and decidability, first appearing in polygons with 7 and 12 sides.

Date & Time

June 06, 2024 | 2:00pm – 3:00pm


Princeton University McDonnell A02


Curtis McMullen, Harvard University