Billiards on regular polygons

Abstract: Imagine that you hit a ball in a pentagon-shaped billiard table, and after bouncing around for a while, the ball comes back to where it started and then repeats its path. I've been studying these "periodic" paths for a couple of years, and it turns out that they're very beautiful, like mathematical art. I'll show lots of pictures, and explain the math behind them. We've been studying the pentagon for many years. For spring break in March, I went to France to work with my collaborator Samuel Lelièvre, and I ended up staying there for three months due to the pandemic, during which time we extended our work to any regular polygon with an odd number of sides. Bring your favorite numbers, and I'll show you the corresponding paths on the spot!

Mathematics

Audience: general audience

University of Glasgow's distinguished lecture series