Ebook: Microlocal methods in mathematical physics and global analysis

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. Read more... Semiclassical and adiabatic limits -- Local Smoothing with a Prescribed Loss for the Schrödinger Equation / Hans Christianson, Jared Wunsch -- Propagation Through Trapped Sets and Semiclassical Resolvent Estimates / Kiril Datchev, András Vasy -- Space-Adiabatic Theory for Random-Landau Hamiltonian: Results and Prospects / Giuseppe De Nittis -- Microlocal Analysis of FIOs with Singularities / Raluca Felea -- A Nonlinear Adiabatic Theorem for Coherent States / Clotilde Fermanian Kammerer, Rémi Carles -- Adiabatic Limits and Related Lattice Point Problems / Yuri A. Kordyukov, Andrey A. Yakovlev -- The Effective Hamiltonian in Curved Quantum Waveguides and When It Does Not Work / David Krejčiřík, Helena Šediváková -- The Adiabatic Limit of the Laplacian on Thin Fibre Bundles / Jonas Lampart, Stefan Teufel -- Adiabatic Limit with Isolated Degenerate Fibres / Richard B. Melrose -- Microlocal Analysis and Adiabatic Problems: The Case of Perturbed Periodic Schrödinger Operators / Gianluca Panati -- Recent Results in Semiclassical Approximation with Rough Potentials / T. Paul -- Singular spaces -- On the Closure of Elliptic Wedge Operators / Juan B. Gil, Thomas Krainer, Gerardo A. Mendoza -- Generalized Blow-Up of Corners and Fiber Products / Chris Kottke, Richard Melrose -- Trace Expansions for Elliptic Cone Operators / Thomas Krainer, Juan B. Gil, Gerardo A. Mendoza -- Spectral Geometry for the Riemann Moduli Space / Rafe Mazzeo -- Invariant Integral Operators on the Oshima Compactification of a Riemannian Symmetric Space: Kernel Asymptotics and Regularized Traces / Pablo Ramacher, Aprameyan Parthasarathy -- Pseudodifferential Operators on Manifolds with Foliated Boundaries / Frédéric Rochon -- The Determinant of the Laplacian on a Conically Degenerating Family of Metrics / David A. Sher -- Spectral and scattering theory -- Relatively Isospectral Noncompact Surfaces / Pierre Albin, Clara Aldana, Frédéric Rochon -- Microlocal Analysis of Scattering Data for Nested Conormal Potentials / Suresh Eswarathasan -- Equidistribution of Eisenstein Series for Convex Co-compact Hyperbolic Manifolds / Colin Guillarmou, Frédéric Naud -- Lower Bounds for the Counting Function of an Integral Operator / Yuri Safarov -- The Identification Problems in SPECT: Uniqueness, Non-uniqueness and Stability / Plamen Stefanov -- Eigenvalues and Spectral Determinants on Compact Hyperbolic Surfaces / Alexander Strohmaier, Ville Uski -- Wave propagation and topological applications -- A Support Theorem for a Nonlinear Radiation Field / Dean Baskin, António Sá Barreto -- Propagation of Singularities Around a Lagrangian Submanifold of Radial Points / Nick Haber, András Vasy -- Local Energy Decay for Several Evolution Equations on Asymptotically Euclidean Manifolds / Dietrich Häfner, Jean-François Bony -- Rayleigh Surface Waves and Geometric Pseudo-differential Calculus / Sönke Hansen -- Topological Implications of Global Hypoellipticity / Gerardo A. Mendoza -- Chern-Simons Line Bundle on Teichmüller Space / Sergiu Moroianu, Colin Guillarmou -- A Simple Diffractive Boundary Value Problem on an Asymptotically Anti-de Sitter Space / Ha Pham -- Quantization in a Magnetic Field / Radu Purice, Viorel Iftimie, Marius Măntoiu -- Price's Law on Black Hole Space-Times / Daniel Tataru