Title: Inverse Spectral Problems
Organizer(s): Hamid Hezari, MIT
Peter Kuchment, Texas A&M University
Speakers: Yaroslav Vorobets, Texas A&M University
Laplacians isospectral under multiple boundary conditions

Ruth Gornet, University of Texas Arlington
The eta invariant on Nilmanifolds

Hamid Hezari, MIT
Spectral rigidity of the ellipse

Gregory Berkolaiko, Texas A&M University
Nodal count of eigenfunctions and stability of nodal partitions

Steve Zelditch, Northwestern University (Cancelled)
Abstract: The special inverse spectral problem of Kac: "Can one hear the shape of a drum?" is to determine a Euclidean domain up to isometry from the spectrum of its Laplacian with Dirichlet, Neumann or more general boundary conditions. Physically, the motivation for this problem is to identify distant physical objects, such as stars or atoms, from the light or sound they emit. This question is generalized to any Riemannian manifold with boundary or without boundary and one can ask "does the spectrum of Laplacian (or Schr\"odinger operator) determine the metric (or potential) up to isometry?" If no, what is a counterexample? or in general extract as much as information possible about the metric (potential) from the spectrum. In this mini-symposium some recent developments in inverse spectrum problems will be discussed.

Please address administrative questions to Scientific questions should be addressed to the chair of the Scientific Program Committee: rundell AT

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