Saturday Evening Plenary Lecture:

"You can't hear the shape of a drum"

Abstract:
In spectroscopy, one attempts to determine the chemical composition of an object such as a star from the characteristic frequencies of emitted light. Analogously, one asks the extent to which the shape of a vibrating membrane, e.g., a drumhead, is encoded in the characteristic frequencies of vibration. In the words of Mark Kac, "Can one hear the shape of a drum?" We will look both at positive answers, e.g., a round drum has no imposters, and negative answers. In particular, we will construct exotic shaped sound-alike drums. We will also listen to Dennis DeTurck's simulation of the sounds of these drums.