Carolyn S.
Gordon
AWM Emmy Noether Lecture
January 2010
San Francisco, CA
Abstract.
Inverse spectral problems ask how much
information about an object is encoded in spectral data. For example, Mark
Kac's question “Can you hear the shape of a drum?" asks whether a plane
domain, viewed as a vibrating membrane, is determined by the Dirichlet
eigenvalue spectrum of the associated Laplacian, equivalently, by the
characteristic frequencies of vibration. The lecture will focus on Kac's
question and its generalization to Riemannian manifolds. We will consider
methods for constructing manifolds with the same spectral data and compare
examples of such “soundalike” manifolds. We will also refer to related
constructions on discrete and quantum graphs.
