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Intro; Preface; Algebraic Microlocal Analysis; Analytic Microlocal Analysis; References; Contents; Part I Algebraic Microlocal Analysis; Procesi Bundles and Symplectic Reflection Algebras; 1 Introduction; 1.1 Procesi Bundles: Hilbert Scheme Case; 1.2 Quotient Singularities and Symplectic Resolutions; 1.3 Procesi Bundles: General Case; 1.4 Symplectic Reflection Algebras; 1.5 Notation and Conventions; 2 Quantizations; 2.1 Algebra Level; 2.2 Sheaf Level; 2.3 Modules Over Quantizations; 2.4 Frobenius Constant Quantizations; 3 Hamiltonian Reductions; 3.1 Classical Hamiltonian Reduction
3.2 Quantum Hamiltonian Reduction3.3 Quantum Hamiltonian Reduction for Frobenius Constant Quantizations; 4 Existence and classification of Procesi bundles; 4.1 Construction of Procesi Bundles; 4.2 Symplectic Reflection Algebras; 4.3 Proof of the Isomorphism Theorem; 4.4 Classification of Procesi bundles; 5 Macdonald positivity and categories mathcalO; 5.1 Derived equivalence; 5.2 Category mathcalO; 5.3 Macdonald positivity; 5.4 Localization theorem; References; Three Lectures on Algebraic Microlocal Analysis; 1 Lecture 1: Microlocalization of Sheaves; 1.1 Generalized Functions
1.2 Microlocalization1.3 Microsupport; 1.4 The Functor µhom; 1.5 An Application: Elliptic Pairs; 2 Lecture 2: Microlocal Euler Classes and Hochschild Homology; 2.1 Hochschild Homology on Complex Manifolds; 2.2 Microlocal Homology; 2.3 Trace Kernels and Microlocal Euler Classes; 2.4 Microlocal Euler Class of Constructible Sheaves; 2.5 Microlocal Euler Class of mathscrD-Modules; 2.6 Microlocal Euler Class of Elliptic Pairs; 3 Lecture 3: Ind-Sheaves and Applications to mathscrD-Modules; 3.1 Ind-Sheaves; 3.2 Sheaves on the Subanalytic Site; 3.3 Moderate and Formal Cohomology
3.4 Applications to mathscrD-Modules I3.5 Applications to mathscrD-Modules II; References; Microlocal Condition for Non-displaceability; 1 Introduction; 2 Generalities; 2.1 Unbounded Derived Category; 2.2 Sheaves on XtimesmathbbR; 3 Non-displaceability Condition; 3.1 Disjoint Supports; 3.2 Hamiltonian Shifts; 4 Non-dispaceability of Certain Lagrangian Submanifolds in mathbbCPn; 4.1; 4.2 Proof of Proposition 4.7; 4.3 Proof of Proposition 4.8; 5 Proof of Proposition 4.4: Constructing umathcalO; 5.1 Constructing umathcalO; 5.2 Proof of Proposition 4.4 (1); 5.3 Proof of Proposition 5.2; 5.4
3.2 Quantum Hamiltonian Reduction3.3 Quantum Hamiltonian Reduction for Frobenius Constant Quantizations; 4 Existence and classification of Procesi bundles; 4.1 Construction of Procesi Bundles; 4.2 Symplectic Reflection Algebras; 4.3 Proof of the Isomorphism Theorem; 4.4 Classification of Procesi bundles; 5 Macdonald positivity and categories mathcalO; 5.1 Derived equivalence; 5.2 Category mathcalO; 5.3 Macdonald positivity; 5.4 Localization theorem; References; Three Lectures on Algebraic Microlocal Analysis; 1 Lecture 1: Microlocalization of Sheaves; 1.1 Generalized Functions
1.2 Microlocalization1.3 Microsupport; 1.4 The Functor µhom; 1.5 An Application: Elliptic Pairs; 2 Lecture 2: Microlocal Euler Classes and Hochschild Homology; 2.1 Hochschild Homology on Complex Manifolds; 2.2 Microlocal Homology; 2.3 Trace Kernels and Microlocal Euler Classes; 2.4 Microlocal Euler Class of Constructible Sheaves; 2.5 Microlocal Euler Class of mathscrD-Modules; 2.6 Microlocal Euler Class of Elliptic Pairs; 3 Lecture 3: Ind-Sheaves and Applications to mathscrD-Modules; 3.1 Ind-Sheaves; 3.2 Sheaves on the Subanalytic Site; 3.3 Moderate and Formal Cohomology
3.4 Applications to mathscrD-Modules I3.5 Applications to mathscrD-Modules II; References; Microlocal Condition for Non-displaceability; 1 Introduction; 2 Generalities; 2.1 Unbounded Derived Category; 2.2 Sheaves on XtimesmathbbR; 3 Non-displaceability Condition; 3.1 Disjoint Supports; 3.2 Hamiltonian Shifts; 4 Non-dispaceability of Certain Lagrangian Submanifolds in mathbbCPn; 4.1; 4.2 Proof of Proposition 4.7; 4.3 Proof of Proposition 4.8; 5 Proof of Proposition 4.4: Constructing umathcalO; 5.1 Constructing umathcalO; 5.2 Proof of Proposition 4.4 (1); 5.3 Proof of Proposition 5.2; 5.4