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Microlocal Methods in Mathematical Physics and Global Analysis

  • Daniel Grieser
  • Stefan Teufel
  • Andras Vasy
Conference proceedings

Part of the Trends in Mathematics book series (TM)

Also part of the Research Perspectives book sub series (RESPERSP)

Table of contents

  1. Front Matter
    Pages i-ix
    PDF

  2. Semiclassical and Adiabatic Limits

    1. Front Matter
      Pages 1-1
      PDF
    2. Local Smoothing with a Prescribed Loss for the Schrödinger Equation
      Hans Christianson, Jared Wunsch
      Pages 3-6
    3. Propagation Through Trapped Sets and Semiclassical Resolvent Estimates
      Kiril Datchev, András Vasy
      Pages 7-10
    4. Space–Adiabatic Theory for Random–Landau Hamiltonian: Results and Prospects
      Giuseppe De Nittis
      Pages 11-14
    5. Microlocal Analysis of FIOs with Singularities
      Raluca Felea
      Pages 15-17
    6. A Nonlinear Adiabatic Theorem for Coherent States
      Clotilde Fermanian Kammerer, Rémi Carles
      Pages 19-23
    7. Adiabatic Limits and Related Lattice Point Problems
      Yuri A. Kordyukov, Andrey A. Yakovlev
      Pages 25-28
    8. The Effective Hamiltonian in Curved Quantum Waveguides and When It Does Not Work
      David Krejčiřík, Helena Šediváková
      Pages 29-32
    9. The Adiabatic Limit of the Laplacian on Thin Fibre Bundles
      Jonas Lampart, Stefan Teufel
      Pages 33-36
    10. Adiabatic Limit with Isolated Degenerate Fibres
      Richard B. Melrose
      Pages 37-43
    11. Microlocal Analysis and Adiabatic Problems: The Case of Perturbed Periodic Schrödinger Operators
      Gianluca Panati
      Pages 45-48
    12. Recent Results in Semiclassical Approximation with Rough Potentials
      T. Paul
      Pages 49-52

  3. Singular spaces

    1. Front Matter
      Pages 53-53
      PDF
    2. On the Closure of Elliptic Wedge Operators
      Juan B. Gil, Thomas Krainer, Gerardo A. Mendoza
      Pages 55-58
    3. Generalized Blow-Up of Corners and Fiber Products
      Chris Kottke, Richard Melrose
      Pages 59-62
    4. Trace Expansions for Elliptic Cone Operators
      Thomas Krainer, Juan B. Gil, Gerardo A. Mendoza
      Pages 63-67
    5. Spectral Geometry for the Riemann Moduli Space
      Rafe Mazzeo
      Pages 69-72
    6. Invariant Integral Operators on the Oshima Compactification of a Riemannian Symmetric Space: Kernel Asymptotics and Regularized Traces
      Pablo Ramacher, Aprameyan Parthasarathy
      Pages 73-76
    7. Pseudodifferential Operators on Manifolds with Foliated Boundaries
      Frédéric Rochon
      Pages 77-80
    8. The Determinant of the Laplacian on a Conically Degenerating Family of Metrics
      David A. Sher
      Pages 81-84

  4. Spectral and Scattering Theory

    1. Front Matter
      Pages 85-85
      PDF
    2. Relatively Isospectral Noncompact Surfaces
      Pierre Albin, Clara Aldana, Frédéric Rochon
      Pages 87-89
    3. Microlocal Analysis of Scattering Data for Nested Conormal Potentials
      Suresh Eswarathasan
      Pages 91-94
    4. Equidistribution of Eisenstein Series for Convex Co-compact Hyperbolic Manifolds
      Colin Guillarmou, Frédéric Naud
      Pages 95-98
    5. Lower Bounds for the Counting Function of an Integral Operator
      Yuri Safarov
      Pages 99-102
    6. The Identification Problems in SPECT: Uniqueness, Non-uniqueness and Stability
      Plamen Stefanov
      Pages 103-104
    7. Eigenvalues and Spectral Determinants on Compact Hyperbolic Surfaces
      Alexander Strohmaier, Ville Uski
      Pages 105-107

  5. Wave Propagation and Topological Applications

    1. Front Matter
      Pages 109-109
      PDF
    2. A Support Theorem for a Nonlinear Radiation Field
      Dean Baskin, António Sá Barreto
      Pages 111-112
    3. Propagation of Singularities Around a Lagrangian Submanifold of Radial Points
      Nick Haber, András Vasy
      Pages 113-116
    4. Local Energy Decay for Several Evolution Equations on Asymptotically Euclidean Manifolds
      Dietrich Häfner, Jean-François Bony
      Pages 117-120
    5. Rayleigh Surface Waves and Geometric Pseudo-differential Calculus
      Sönke Hansen
      Pages 121-124
    6. Topological Implications of Global Hypoellipticity
      Gerardo A. Mendoza
      Pages 125-127
    7. Chern-Simons Line Bundle on Teichmüller Space
      Sergiu Moroianu, Colin Guillarmou
      Pages 129-132
    8. A Simple Diffractive Boundary Value Problem on an Asymptotically Anti-de Sitter Space
      Ha Pham
      Pages 133-136
    9. Quantization in a Magnetic Field
      Radu Purice, Viorel Iftimie, Marius Măntoiu
      Pages 137-144
    10. Price’s Law on Black Hole Space-Times
      Daniel Tataru
      Pages 145-148

About these proceedings

Introduction

Microlocal analysis is a mathematical field that was invented for the detailed investigation of problems from partial differential equations in the mid-20th century and that incorporated and elaborated on many ideas that had originated in physics. Since then, it has grown to a powerful machine used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. This book collects extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of Tübingen from June 14th to 18th, 2011.

Keywords

global analysis microlocal analysis semiclassical limit singular spaces spectral theory

Editors and affiliations

  • Daniel Grieser
    • 1
  • Stefan Teufel
    • 2
  • Andras Vasy
    • 3
  1. 1.OldenburgGermany
  2. 2.Inst. MathematikUniversität TübingenTübingenGermany
  3. 3., Department of Mathematics, Bldg. 380Stanford UniversityStanfordUSA

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