Contemporary Mathematics 1994; 299 pp; softcover Volume: 173 ISBN10: 0821851853 ISBN13: 9780821851852 List Price: US$70 Member Price: US$56 Order Code: CONM/173
 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 graphtheoretic analogue, the adjacency matrix, to underlying geometric and topological data. This volume brings together papers presented at the AMSIMSSIAM 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. Readership Research mathematicians. Table of Contents  E. Y. Amiran  An inverse problem and spectral invariants for billards
 J. Angel, S. Poulos, A. Terras, C. Trimble, and E. Velasquez  Spherical functions and transforms on finite upper half planes: Eigenvalues of the combinatorial Laplacian, uncertainty, traces
 R. Brooks  \(L^p\) spectral geometry
 R. Brooks and P. Glezen  An \(L^p\) spectral bootstrap theorem
 X. Dai and G. Wei  Finite part of spectrum and isospectrality
 J. Dodziuk  Nonexistence of universal upper bounds for the first positive eigenvalue of the LaplaceBeltrami operator
 K. Fujiwara  Convergence of the eigenvalues of Laplacians in a class of finite graphs
 C. S. Gordon  Isospectral closed Riemannian manifolds which are not locally isometric, Part II
 R. Gornet  The length spectrum and representation theory on two and threestep nilpotent Lie groups
 E. Gutkin  A few remarks on the billiard ball problem
 L. Ji and S. Zelditch  Hyperbolic cusp forms and spectral simplicity on compact hyperbolic surfaces
 Ya. Kurylev  Inverse boundary problems on Riemannian manifolds
 L. Malozemov  Spectral theory of the differential Laplacian on the modified Koch curve
 Y. Mao  Conjugate geodesic flows in negatively curved manifolds
 H. Pesce  Variétés isospectrales et représentations de groupes
 Y. N. Petridis  On differences of eigenvalues for flat tori and hyperbolic surfaces
 G. Quenell  Combinatorics of free product graphs
 T. Sunada  A discrete analogue of periodic magnetic Schrödinger operators
