# Spectral geometry

- Responsibility
- Alex H. Barnett, Carolyn S. Gordon, Peter A. Perry, Alejandro Uribe, editors.
- Language
- English.
- Publication
- Providence, Rhode Island : American Mathematical Society, 2012.
- Copyright notice
- ©2012
- Physical description
- ix, 339 pages : illustrations ; 26 cm.
- Series
- Proceedings of symposia in pure mathematics ; v. 84.

## Access

## Creators/Contributors

- Meeting
- International Conference on Spectral Geometry (2010 : Dartmouth College)
- Contributor
- Barnett, Alex, 1972 December 7- editor of compilation.

## Contents/Summary

- Bibliography
- Includes bibliographical references.
- Publisher's Summary
- This volume contains the proceedings of the International Conference on Spectral Geometry, held July 19-23, 2010, at Dartmouth College, Dartmouth, New Hampshire. Eigenvalue problems involving the Laplace operator on manifolds have proven to be a consistently fertile area of geometric analysis with deep connections to number theory, physics, and applied mathematics. Key questions include the measures to which eigenfunctions of the Laplacian on a Riemannian manifold condense in the limit of large eigenvalue, and the extent to which the eigenvalues and eigenfunctions of a manifold encode its geometry. In this volume, research and expository articles, including those of the plenary speakers Peter Sarnak and Victor Guillemin, address the flurry of recent progress in such areas as quantum unique ergodicity, isospectrality, semiclassical measures, the geometry of nodal lines of eigenfunctions, methods of numerical computation, and spectra of quantum graphs. This volume also contains mini-courses on spectral theory for hyperbolic surfaces, semiclassical analysis, and orbifold spectral geometry that prepared the participants, especially graduate students and young researchers, for conference lectures.

(source: Nielsen Book Data)

## Subjects

- Subject
- Spectral geometry > Congresses.
- Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Isospectrality.
- Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Spectral problems; spectral geometry; scattering theory.
- Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity.
- Numerical analysis -- Partial differential equations, boundary value problems -- Eigenvalue problems.
- Partial differential equations -- Spectral theory and eigenvalue problems -- Estimation of eigenvalues, upper and lower bounds.
- Number theory -- Discontinuous groups and automorphic forms -- Spectral theory; Selberg trace formula.
- Differential geometry -- Global differential geometry -- Global Riemannian geometry, including pinching.
- Ordinary differential equations -- Ordinary differential operators -- Eigenvalues, estimation of eigenvalues, upper and lower bounds.
- Ordinary differential equations -- Asymptotic theory -- Asymptotic expansions.
- Manifolds and cell complexes -- Differential topology -- Topology and geometry of orbifolds.

## Bibliographic information

- Publication date
- 2012
- Copyright date
- 2012
- Series
- Proceedings of symposia in pure mathematics ; v. 84
- ISBN
- 9780821853191 (alk. paper)
- 0821853198 (alk. paper)