Workshop on spectral problems; July 2010

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AbstractAward: DMS-1005360Principal Investigator: Carolyn S. Gordon, Alexander Barnett, Peter A. PerryA week-long International Conference on Spectral Geometry will be held at Dartmouth College July 19--23, 2010. The primary themes of the conference will be Quantum Unique Ergodicity, which addresses the behavior of the highly excited states in the quantization of ergodic Hamiltonian systems, and Inverse Spectral Geometry, which asks the extent to which spectral data associated with the Laplacian or other natural operators encode the geometry of a Riemannian manifold. In addition to spectral problems on Riemannian manifolds, there will be a secondary focus on the related topic of quantum graphs, in which the one-dimensional Laplacian acts along edges, and waves scatter at vertices.Both quantum unique ergodicity and inverse spectral geometry are areas of intense research activity in mathematics, bridging geometry, analysis and number theory, and both have strong ties to physics. By bringing together experts and young researchers with various perspectives and expertise, the conference will promote new collaborations and interactions and contribute to the advancement of research in these areas. The conference will be preceded by a two-day intensive workshop, aimed at graduate students and recent Ph.D.'s, to prepare for the conference themes.