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.
Mục lục
Part I: Algebraic Microlocal Analysis.- Losev, I.: Procesi Bundles and Symplectic Reflection Algebras.- Schapira, P.: Three Lectures on Algebraic Microlocal Analysis.- Tamarkin, D.: Microlocal Condition for Non-displaceability.- Tsygan, B.: A Microlocal Category Associated to a Symplectic Manifold.- Part II: Analytic Microlocal Analysis.- Berman, R.: Determinantal Point Processes and Fermions on Polarized Complex Manifolds: Bulk Universality.- Berndtsson, B.: Probability Measures Associated to Geodesics in the Space of Kahlermetrics.- Canzani, Y. and Toth, J: Intersection Bounds for Nodal Sets of Laplace Eigenfunctions.- Christ, M.: Upper Bounds for Bergman Kernels Associated to Positive Line Bundles with Smooth Hermitian Metrics.- Christ, M.: Off-diagonal Decay of Bergman Kernels: On a Question of Zelditch.- Hitrik, M. and Sjostrand, J: Two Mini-courses on Analytic Microlocal Analysis.- Lebeau, G.: A Proof of a Result of L. Boutet de Monvel.- Martinez, A., Nakamura, S. and Sordoni, V: Propagation of Analytic Singularities for Short and Long Range Perturbations of the Free Schrodinger Equation.- Zelditch, S. and Zhou, P: Pointwise Weyl Law for Partial Bergman Kernels.- Zworski, M.: Scattering Resonances as Viscosity Limits.
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