Microlocal Methods in Mathematical Physics and Global Analysis

1. Front Matter

   Pages i-ix

   PDF

2. Semiclassical and Adiabatic Limits

   1. Front Matter

      Pages 1-1

      PDF

3. Semiclassical and adiabatic limits

   1. Local Smoothing with a Prescribed Loss for the Schrödinger Equation

      • Hans Christianson, Jared Wunsch

      Pages 3-6

   2. Propagation Through Trapped Sets and Semiclassical Resolvent Estimates

      • Kiril Datchev, András Vasy

      Pages 7-10

   3. Space–Adiabatic Theory for Random–Landau Hamiltonian: Results and Prospects

      • Giuseppe De Nittis

      Pages 11-14

   4. Microlocal Analysis of FIOs with Singularities

      • Raluca Felea

      Pages 15-17

   5. A Nonlinear Adiabatic Theorem for Coherent States

      • Clotilde Fermanian Kammerer, Rémi Carles

      Pages 19-23

   6. Adiabatic Limits and Related Lattice Point Problems

      • Yuri A. Kordyukov, Andrey A. Yakovlev

      Pages 25-28

   7. The Effective Hamiltonian in Curved Quantum Waveguides and When It Does Not Work

      • David Krejčiřík, Helena Šediváková

      Pages 29-32

   8. The Adiabatic Limit of the Laplacian on Thin Fibre Bundles

      • Jonas Lampart, Stefan Teufel

      Pages 33-36

   9. Adiabatic Limit with Isolated Degenerate Fibres

      • Richard B. Melrose

      Pages 37-43

   10. Microlocal Analysis and Adiabatic Problems: The Case of Perturbed Periodic Schrödinger Operators

       • Gianluca Panati

       Pages 45-48

   11. Recent Results in Semiclassical Approximation with Rough Potentials

       • T. Paul

       Pages 49-52

4. 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

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

• global analysis
• microlocal analysis
• semiclassical limit
• singular spaces
• spectral theory
• ordinary differential equations

• Oldenburg, Germany

  Daniel Grieser

• Inst. Mathematik, Universität Tübingen, Tübingen, Germany

  Stefan Teufel

• , Department of Mathematics, Bldg. 380, Stanford University, Stanford, USA

  Andras Vasy

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