Spectral geometry runs through much of contemporary mathematics, drawing on and stimulating developments in such diverse areas as Lie algebras, graph theory, group representation theory, and Riemannian geometry. The aim is to relate the spectrum of the Laplace operator or its graph-theoretic analogue, the adjacency matrix, to underlying geometric and topological data. This volume brings together papers presented at the AMS-IMS-SIAM Joint Summer Research Conference on Spectral Geometry, held in July 1993 at the University of Washington in Seattle. With contributions from some of the top experts in the field, this book presents an excellent overview of current developments in spectral geometry.
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978-0-8218-5185-2 (9780821851852)
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An inverse problem and spectral invariants for billards by E. Y. Amiran Spherical functions and transforms on finite upper half planes: Eigenvalues of the combinatorial Laplacian, uncertainty, traces by J. Angel, S. Poulos, A. Terras, C. Trimble, and E. Velasquez $L^p$ spectral geometry by R. Brooks An $L^p$ spectral bootstrap theorem by R. Brooks and P. Glezen Finite part of spectrum and isospectrality by X. Dai and G. Wei Nonexistence of universal upper bounds for the first positive eigenvalue of the Laplace-Beltrami operator by J. Dodziuk Convergence of the eigenvalues of Laplacians in a class of finite graphs by K. Fujiwara Isospectral closed Riemannian manifolds which are not locally isometric, Part II by C. S. Gordon The length spectrum and representation theory on two and three-step nilpotent Lie groups by R. Gornet A few remarks on the billiard ball problem by E. Gutkin Hyperbolic cusp forms and spectral simplicity on compact hyperbolic surfaces by L. Ji and S. Zelditch Inverse boundary problems on Riemannian manifolds by Ya. Kurylev Spectral theory of the differential Laplacian on the modified Koch curve by L. Malozemov Conjugate geodesic flows in negatively curved manifolds by Y. Mao Varietes isospectrales et representations de groupes by H. Pesce On differences of eigenvalues for flat tori and hyperbolic surfaces by Y. N. Petridis Combinatorics of free product graphs by G. Quenell A discrete analogue of periodic magnetic Schrodinger operators by T. Sunada.
