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Spectral geometry / [electronic resource] Alex H. Barnett, Carolyn S. Gordon, Peter A. Perry, Alejandro Uribe, editors.

By: International Conference on Spectral Geometry (2010 : Dartmouth College)Contributor(s): Barnett, Alex, 1972 December 7- [editor of compilation.]Material type: Text

TextSeries: Proceedings of symposia in pure mathematics ; v. 84Publisher: Providence, Rhode Islands : American Mathematical Society, [2012]Description: 1 online resource (ix, 339 pages : illustrations)Content type: text Media type: unmediated Carrier type: volumeISBN: 9780821891964 (online)Subject(s): 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 orbifoldsAdditional physical formats: Spectral geometry /DDC classification: 516.3/62 LOC classification: QA614.95 | .I58 2010Other classification: 58J53 | 58J50 | 58J51 | 65N25 | 35P15 | 11F72 | 53C20 | 34L15 | 34E05 | 57R18 Online resources: Contents | Contents

Contents:

Introduction to spectral theory on hyperbolic surfaces / David Borthwick -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1347 Orbifolds and their spectra / Carolyn Gordon -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1348 A brief introduction to semiclassical analysis / Alejandro Uribe and Zuoqin Wang -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1349 The dynamics of the Schr�odinger flow from the point of view of semiclassical measures / Nalini Anantharaman and Fabricio Maci�a -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1351 Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths / Gregory Berkolaiko and Peter Kuchment -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1352 Investigating the spectral geometry of a soft wall / Jeffrey Bouas, Stephen Fulling, Fernando Mera, Krishna Thapa, Cynthia Trendafilova and Jef Wagner -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1353 Equivariant inverse spectral problems / Emily B. Dryden, Victor Guillemin and Rosa Sena-Dias -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1354 Classical equivalence and quantum equivalence of magnetic fields on Flat Tori / Carolyn Gordon, William Kirwin, Dorothee Schueth and David Webb -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1355 A semiclassical heat trace expansion for the perturbed harmonic oscillator / Victor Guillemin, Alejandro Uribe and Zuoqin Wang -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1356 Estimates on Neumann eigenfunctions at the boundary, and the "method of particular solutions" for computing them / Andrew Hassell and Alex Barnett -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1357 Recent progress on the quantum unique ergodicity conjecture / Peter Sarnak -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1361 Lower bounds for volumes of nodal sets: An improvement of a result of Sogge-Zelditch / Hamid Hezari and Zuoqin Wang -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1358 The nodal set of a finite sum of Maass cusp forms is a graph / Chris Judge -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1359 Asymptotics of spectral quantities of Schr�odinger operators / Thomas Kappeler, Beat Schaad and Peter Topalov -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1360 On the nodal lines of random and deterministic Laplace eigenfunctions / Igor Wigman -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1362 Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I / Steven Zelditch -- http://www.ams.org/pspum/084 http://dx.doi.org/10.1090/pspum/084/1363

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Includes bibliographical references.

Introduction to spectral theory on hyperbolic surfaces / David Borthwick -- Orbifolds and their spectra / Carolyn Gordon -- A brief introduction to semiclassical analysis / Alejandro Uribe and Zuoqin Wang -- The dynamics of the Schr�odinger flow from the point of view of semiclassical measures / Nalini Anantharaman and Fabricio Maci�a -- Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths / Gregory Berkolaiko and Peter Kuchment -- Investigating the spectral geometry of a soft wall / Jeffrey Bouas, Stephen Fulling, Fernando Mera, Krishna Thapa, Cynthia Trendafilova and Jef Wagner -- Equivariant inverse spectral problems / Emily B. Dryden, Victor Guillemin and Rosa Sena-Dias -- Classical equivalence and quantum equivalence of magnetic fields on Flat Tori / Carolyn Gordon, William Kirwin, Dorothee Schueth and David Webb -- A semiclassical heat trace expansion for the perturbed harmonic oscillator / Victor Guillemin, Alejandro Uribe and Zuoqin Wang -- Estimates on Neumann eigenfunctions at the boundary, and the "method of particular solutions" for computing them / Andrew Hassell and Alex Barnett -- Recent progress on the quantum unique ergodicity conjecture / Peter Sarnak -- Lower bounds for volumes of nodal sets: An improvement of a result of Sogge-Zelditch / Hamid Hezari and Zuoqin Wang -- The nodal set of a finite sum of Maass cusp forms is a graph / Chris Judge -- Asymptotics of spectral quantities of Schr�odinger operators / Thomas Kappeler, Beat Schaad and Peter Topalov -- On the nodal lines of random and deterministic Laplace eigenfunctions / Igor Wigman -- Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I / Steven Zelditch --