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Mathematics Colloquium


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


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