Colloquium: "You Can Hear the Shape of a Billiard Table"

Abstract: Kac famously asked if you can “hear the shape of a drum”-- what geometric information about a plane domain can be read off of the spectrum of its Laplacian? I’ll talk about a parallel question in symbolic dynamics: if you have a polygonal domain and all you know is the sequence of sides that can be struck by a traveling billiard ball, can you guess the polygon? (For example, if two sides A and B are parallel, then you can have a sequence that repeats ABAB... forever.) . I’ll describe a surprisingly strong rigidity result: for instance, you can “hear the shape of a pentagon.”

Hosts: Aliakbar Daemi and Ari Stern