Graduate Student Seminar, 4:30pm ___, 2003



Can one hear the shape of a drum?


In 1966, Mark Kac posed the following question: "Can one hear the shape of a drum?". He had in mind the following problem: View the surface of a drum as a plane domain M, and say that $\lambda$ is in the spectrum of M if exists a nonzero function f with $\Delta f = \lamda f$ and f=0 on the boundary. These eigenvalues determine the frequency of sound provided by M. If you could "hear" the spectrum of M what geometrical information can you obtain about M?

We will answer this and many other related questions and try to give a survey of the field known as Spectral Geometry. We shall discuss the beautiful result of Sunada and Buser's example which were a key development to Carolyn Gordon's answer to Kac's question. It is important to notice that a lot of work in this subject is done in the compact case. We will address the noncompact case and see what are the appropriate questions and current developments.

To volunteer to give a talk, or for any other questions regarding this schedule, contact Wesley Calvert