Mathematics Department Colloquium: You can hear the shape of a billiard table

Colloquium | September 27 | 4:10-5 p.m. | 60 Evans Hall

 Moon Duchin, Tufts

 Department of Mathematics

A great deal of fundamental mathematics has been directed at the question of "hearing the shape of a drum," or reading geometric features of a plane domain or manifold off from its Laplace spectrum. I'll address a parallel question in symbolic dynamics: if you have a Euclidean polygon and only know the sequences of sides struck in succession by billiard trajectories—that is, the bounce spectrum—does it determine the polygon? Spoiler: The answer is basically yes. This is joint work with Erlandsson, Leininger, and Sadanand.