Time: 4:00 p.m.
Location: 106 McAllister Building
Name: Richard Schwartz
Affiliation: Brown University
Title: Unbounded orbits for outer billiards
Abstract: Outer billiards is a basic dynamical system defined relative to a convex planar shape. This system was introduced in the 1950s by B.H. Neumann and later popularized in the 1970s by J. Moser. All along, one of the central questions has been: Does there exist an outer billiards system with some unbounded orbits? I will show that outer billiards has some unbounded orbits when it is defined relative to the Penrose kite, the quadrilateral that appears in the famous Penrose tiling. My proof relates the problem to self-similar tilings, polygon exchange maps, and arithmetic dynamics.
