Speaker
Curtis McMullen
(Harvard University)
Description
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.
