Algebraic and Analytic Microlocal Analysis: AAMA, Evanston, Illinois, USA, 2012 and 2013

Description

This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University. Featured papers expand on mini-courses and talks ranging from foundational material to advanced research-level papers, and new applications in symplectic geometry, mathematical physics, partial differential equations, and complex analysis are discussed in detail. Topics include Procesi bundles and symplectic reflection algebras, microlocal condition for non-displaceability, polarized complex manifolds, nodal sets of Laplace eigenfunctions, geodesics in the space of Kӓhler metrics, and partial Bergman kernels. This volume is a valuable resource for graduate students and researchers in mathematics interested in understanding microlocal analysis and learning about recent research in the area. Front Matter ....Pages i-xvi Front Matter ....Pages 1-1 Procesi Bundles and Symplectic Reflection Algebras (Ivan Losev)....Pages 3-61 Three Lectures on Algebraic Microlocal Analysis (Pierre Schapira)....Pages 63-97 Microlocal Condition for Non-displaceability (Dmitry Tamarkin)....Pages 99-223 A Microlocal Category Associated to a Symplectic Manifold (Boris Tsygan)....Pages 225-337 Front Matter ....Pages 339-339 Determinantal Point Processes and Fermions on Polarized Complex Manifolds: Bulk Universality (Robert J. Berman)....Pages 341-393 Probability Measures Associated to Geodesics in the Space of Kähler Metrics (Bo Berndtsson)....Pages 395-419 Intersection Bounds for Nodal Sets of Laplace Eigenfunctions (Yaiza Canzani, John A. Toth)....Pages 421-436 Upper Bounds for Bergman Kernels Associated to Positive Line Bundles with Smooth Hermitian Metrics (Michael Christ)....Pages 437-457 Off-Diagonal Decay of Bergman Kernels: On a Question of Zelditch (Michael Christ)....Pages 459-481 Two Minicourses on Analytic Microlocal Analysis (Michael Hitrik, Johannes Sjöstrand)....Pages 483-540 A Proof of a Result of L. Boutet de Monvel (Gilles Lebeau)....Pages 541-574 Propagation of Analytic Singularities for Short and Long Range Perturbations of the Free Schrödinger Equation (André Martinez, Shu Nakamura, Vania Sordoni)....Pages 575-587 Pointwise Weyl Law for Partial Bergman Kernels (Steve Zelditch, Peng Zhou)....Pages 589-634 Scattering Resonances as Viscosity Limits (Maciej Zworski)....Pages 635-654