Billiards and the Arithmetic of Non-Arithmetic Groups
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
Speakers
Curtis McMullen, Harvard University
Affiliation
Harvard University