**Proceedings of Symposia in Pure Mathematics**

Volume: 84;
2012;
339 pp;
Hardcover

MSC: Primary 58; 65; 35; 11; 53; 34; 57;

Print ISBN: 978-0-8218-5319-1

Product Code: PSPUM/84

List Price: $80.00

AMS Member Price: $64.00

MAA Member Price: $72.00

**Electronic ISBN: 978-0-8218-9196-4
Product Code: PSPUM/84.E**

List Price: $80.00

AMS Member Price: $64.00

MAA Member Price: $72.00

# Spectral Geometry

Share this page *Edited by *
*Alex H. Barnett; Carolyn S. Gordon; Peter A. Perry; Alejandro Uribe*

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.

#### Readership

Graduate students and research mathematicians interested in Riemannian geometry and analysis on manifolds.

# Table of Contents

## Spectral Geometry

- Contents v6 free
- Preface vii8 free
- PART I. EXPOSITORY LECTURES 112 free
- PART II. INVITED PAPERS 91102
- The dynamics of the Schrödinger flow from the point of view of semiclassical measures 93104
- Dependence of the Spectrum of a Quantum Graph on Vertex Conditions and Edge Lengths 117128
- Investigating the spectral geometry of a soft wall 139150
- Equivariant Inverse Spectral Problems 155166
- Classical Equivalence and Quantum Equivalence of Magnetic Fields on Flat Tori 167178
- A semiclassical heat trace expansion for the perturbed harmonic oscillator 181192
- Estimates on Neumann eigenfunctions at the boundary, and the “Method of Particular Solutions” for computing them 195206
- Recent progress on the Quantum Unique Ergodicity Conjecture 211222
- Lower bounds for volumes of nodal sets: an improvement of a result of Sogge-Zelditch 229240
- The nodal set of a finite sum of Maass cusp forms is a graph 237248
- Asymptotics of spectral quantities of Schrödinger operators 243254
- On the nodal lines of random and deterministic Laplace eigenfunctions 285296
- Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I 299310