Speaker: W. Patrick Hooper, SUNY at Stony Brook
Title of talk: Stable Billiards in Acute and Obtuse Triangles
Abstract: The symbolicdynamics of a periodic billiard path in a triangle is the sequence of edges thebilliard ball hits. We say a periodic billiard path in a triangle T is"stable" if there is an open neighborhood U of triangles containing T, so thatfor all T' in U we can find a periodic billiard path in T' withthe same symbolic dynamics.

We will discuss the proof of thefollowing theorem: No right triangle admits stableperiodic billiard paths. Moreover, a stable periodic billiardpath in an acute triangle never has the same symbolic dynamicsas a stable periodic billiard path in an obtuse triangle.

Perhaps surprisingly, the proof isessentially topological.