Analysis, Dynamics, and Applications Seminar

This talk is about Kac‘s famous inverse problem from 1966: “Can one hear the shape of a drum?“ The question asks whether the frequencies of vibration of a bounded domain determine the shape of the domain. First, we present a quick survey on the known results. Then we discuss the key connection between eigenvalues of the Laplacian and the dynamics of the billiard, which is governed by the so called “Poisson Summation Formula“. Finally, we discuss our main theorem that “one can hear the shape of nearly circular ellipses“. This is a joint work with Steve Zelditch.