Polygonal billiards and translation surfaces
Time and place
12 PM on Tuesday, April 7th, 2009; NAC 1/511E
Dr. W. Pat Hooper (Northwestern University)
Abstract
I will discuss the dynamical system of a billiard ball bouncing around inside a polygon. A polygon is called rational if all its angles are rational multiples of pi. A polygon is irrational otherwise. Billiards in rational polygons are quite well understood, however not much is known about the irrational case. The study of billiards in polygons is closely connected to the study of translation surfaces, which are surfaces constructed by gluing together polygons in the plane by translations. This connection will reveal why billiards in irrational polygons are so difficult to understand. I will discuss progress on some of the open problems in this area.
