Hardcover ISBN:  9780821853191 
Product Code:  PSPUM/84 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Electronic ISBN:  9780821891964 
Product Code:  PSPUM/84.E 
List Price:  $80.00 
MAA Member Price:  $72.00 
AMS Member Price:  $64.00 

Book DetailsProceedings of Symposia in Pure MathematicsVolume: 84; 2012; 339 ppMSC: Primary 58; 65; 35; 11; 53; 34; 57;
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 minicourses 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.ReadershipGraduate students and research mathematicians interested in Riemannian geometry and analysis on manifolds.

Table of Contents

Part I. Expository Lectures

David Borthwick  Introduction to spectral theory on hyperbolic surfaces

Carolyn Gordon  Orbifolds and their spectra

Alejandro Uribe and Zuoqin Wang  A brief introduction to semiclassical analysis

Part II. Invited Papers

Nalini Anantharaman and Fabricio Macià  The dynamics of the Schrödinger flow from the point of view of semiclassical measures

Gregory Berkolaiko and Peter Kuchment  Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths

Jeffrey Bouas, Stephen Fulling, Fernando Mera, Krishna Thapa, Cynthia Trendafilova and Jef Wagner  Investigating the spectral geometry of a soft wall

Emily B. Dryden, Victor Guillemin and Rosa SenaDias  Equivariant inverse spectral problems

Carolyn Gordon, William Kirwin, Dorothee Schueth and David Webb  Classical equivalence and quantum equivalence of magnetic fields on Flat Tori

Victor Guillemin, Alejandro Uribe and Zuoqin Wang  A semiclassical heat trace expansion for the perturbed harmonic oscillator

Andrew Hassell and Alex Barnett  Estimates on Neumann eigenfunctions at the boundary, and the “method of particular solutions” for computing them

Peter Sarnak  Recent progress on the quantum unique ergodicity conjecture

Hamid Hezari and Zuoqin Wang  Lower bounds for volumes of nodal sets: An improvement of a result of SoggeZelditch

Chris Judge  The nodal set of a finite sum of Maass cusp forms is a graph

Thomas Kappeler, Beat Schaad and Peter Topalov  Asymptotics of spectral quantities of Schrödinger operators

Igor Wigman  On the nodal lines of random and deterministic Laplace eigenfunctions

Steven Zelditch  Pluripotential theory on Grauert tubes of real analytic Riemannian manifolds, I


Additional Material

Request Review Copy

Get Permissions
 Book Details
 Table of Contents
 Additional Material

 Request Review Copy
 Get Permissions
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 minicourses 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.
Graduate students and research mathematicians interested in Riemannian geometry and analysis on manifolds.

Part I. Expository Lectures

David Borthwick  Introduction to spectral theory on hyperbolic surfaces

Carolyn Gordon  Orbifolds and their spectra

Alejandro Uribe and Zuoqin Wang  A brief introduction to semiclassical analysis

Part II. Invited Papers

Nalini Anantharaman and Fabricio Macià  The dynamics of the Schrödinger flow from the point of view of semiclassical measures

Gregory Berkolaiko and Peter Kuchment  Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths

Jeffrey Bouas, Stephen Fulling, Fernando Mera, Krishna Thapa, Cynthia Trendafilova and Jef Wagner  Investigating the spectral geometry of a soft wall

Emily B. Dryden, Victor Guillemin and Rosa SenaDias  Equivariant inverse spectral problems

Carolyn Gordon, William Kirwin, Dorothee Schueth and David Webb  Classical equivalence and quantum equivalence of magnetic fields on Flat Tori

Victor Guillemin, Alejandro Uribe and Zuoqin Wang  A semiclassical heat trace expansion for the perturbed harmonic oscillator

Andrew Hassell and Alex Barnett  Estimates on Neumann eigenfunctions at the boundary, and the “method of particular solutions” for computing them

Peter Sarnak  Recent progress on the quantum unique ergodicity conjecture

Hamid Hezari and Zuoqin Wang  Lower bounds for volumes of nodal sets: An improvement of a result of SoggeZelditch

Chris Judge  The nodal set of a finite sum of Maass cusp forms is a graph

Thomas Kappeler, Beat Schaad and Peter Topalov  Asymptotics of spectral quantities of Schrödinger operators

Igor Wigman  On the nodal lines of random and deterministic Laplace eigenfunctions

Steven Zelditch  Pluripotential theory on Grauert tubes of real analytic Riemannian manifolds, I