| Date: Tuesday, March 24, 2009
Title: When you can't hear the shape of a manifold
Abstract: Mark Kac's question "Can you hear the shape of a drum?" asks the extent to which
the geometry of a plane domain, viewed as a vibrating membrane, is encoded in
the Dirichlet eigenvalue spectrum of the associated Laplacian, equivalently, in
the characteristic frequencies of vibration. More generally, one asks the
extent to which spectral data on a Riemannian manifold encodes the geometry.
We will survey techniques for constructing manifolds with the same spectral data
and look at examples in order to identify geometric invariants that are not
spectrally determined.
Speaker: Carolyn Gordon
Institution: Dartmouth College
|
