Arbeitstagung Bonn 2013 : In Memory of Friedrich Hirzebruch

By: Ballmann, WernerContributor(s): Blohmann, Christian | Faltings, Gerd | Teichner, PeterMaterial type: TextTextSeries: eBooks on DemandProgress in Mathematics: Publisher: Cham : Springer International Publishing, 2016Description: 1 online resource (427 p.)ISBN: 9783319436487Subject(s): MathematiciansGenre/Form: Electronic books.Additional physical formats: Print version:: Arbeitstagung Bonn 2013 : In Memory of Friedrich HirzebruchDDC classification: 510 LOC classification: QA1-939Online resources: Click here to view this ebook.
Contents:
Preface -- Contents -- Contributors -- The Hirzebruch Signature Theorem for Conical Metrics -- 1 Introduction -- 2 Multiplicative Genera -- 3 Cones -- 4 Globalizing the Argument -- References -- Depth and the Local Langlands Correspondence -- 1 Introduction -- 2 The Local Langlands Correspondence for Inner Formsof GLn(F) -- 2.1 The Statement of the Correspondence -- 2.2 The Jacquet-Langlands Correspondence -- 2.3 Depth for Langlands Parameters -- 2.4 The Depth of Representations of GLm(D) -- 2.5 Conductors of Representations of GLm (D) -- 2.6 Depth Preservation
3 The Local Langlands Correspondence for Inner Formsof SLn(F) -- 3.1 The Statement of the Correspondence -- 3.2 The Depth of Representations of GLm (D)der -- 3.3 The Depth of Langlands Parameters for GLm (D)der -- References -- Guide to Elliptic Boundary Value Problems for Dirac-Type Operators -- 1 Introduction -- 2 Preliminaries -- 2.1 Differential Operators -- 2.2 The Principal Symbol -- 2.3 Elliptic Operators -- 3 Dirac-Type Operators -- 3.1 Clifford Relations and Dirac-Type Operators -- 3.2 Adapted Operators on the Boundary -- 3.3 Formally Self-adjoint Dirac-Type Operators
4 Boundary Value Problems -- 4.1 Spectral Subspaces -- 4.2 The Maximal Domain -- 4.3 Boundary Conditions -- 4.4 D-Elliptic Boundary Conditions -- 4.5 Self-adjoint D-Elliptic Boundary Conditions -- 4.6 Local and Pseudo-Local Boundary Conditions -- 4.7 Examples -- 5 Spectral Theory -- 5.1 Coercivity at Infinity -- 5.2 Coercivity with Respect to a Boundary Condition -- 6 Index Theory -- 6.1 Fredholm Property and Index Formulas -- 6.2 Relative Index Theory -- 6.3 Boundary Chiralities and Index -- Appendix 1: Dirac Operators in the Sense of Gromov and Lawson
Appendix 2: Proofs of Some Auxiliary Results -- References -- Symplectic and Hyperkähler Implosion -- 1 Introduction -- 2 Symplectic Quivers -- 3 Hyperkähler Quiver Diagrams -- 4 Properties of Hyperkähler Implosion -- 5 Hyperkähler Implosion for Special Orthogonal and Symplectic Groups -- References -- Kazhdan-Lusztig Conjectures and Shadows of Hodge Theory -- 1 Introduction -- 2 Intersection Cohomology and the Decomposition Theorem -- 3 Schubert Varieties and Bott-Samelson Resolutions -- 4 Soergel Modules and Intersection Cohomology -- 5 Soergel Modules for Arbitrary Coxeter Systems
6 The Flag Variety of a Dihedral Group -- 6.1 Gauß's q-Numbers -- 6.2 The Reflection Representation of a Dihedral Group -- 6.3 Schubert Calculus -- References -- Uniform Sup-Norm Bounds on Average for Cusp Forms of Higher Weights -- 1 Introduction -- 1.1 Motivation -- 1.2 Statement of Results -- 1.3 Related Results -- 1.4 Outline of the Paper -- 2 Background Material -- 2.1 Hyperbolic Metric -- 2.2 Cusp Forms of Higher Weights -- 2.3 Maass Forms of Higher Weights -- 2.4 Heat Kernels of Higher Weights -- 2.5 Spectral Expansions -- 3 Heat Kernel Analysis -- 4 Bounds in the Cocompact Setting
5 Bounds in the Cofinite Setting
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Preface -- Contents -- Contributors -- The Hirzebruch Signature Theorem for Conical Metrics -- 1 Introduction -- 2 Multiplicative Genera -- 3 Cones -- 4 Globalizing the Argument -- References -- Depth and the Local Langlands Correspondence -- 1 Introduction -- 2 The Local Langlands Correspondence for Inner Formsof GLn(F) -- 2.1 The Statement of the Correspondence -- 2.2 The Jacquet-Langlands Correspondence -- 2.3 Depth for Langlands Parameters -- 2.4 The Depth of Representations of GLm(D) -- 2.5 Conductors of Representations of GLm (D) -- 2.6 Depth Preservation

3 The Local Langlands Correspondence for Inner Formsof SLn(F) -- 3.1 The Statement of the Correspondence -- 3.2 The Depth of Representations of GLm (D)der -- 3.3 The Depth of Langlands Parameters for GLm (D)der -- References -- Guide to Elliptic Boundary Value Problems for Dirac-Type Operators -- 1 Introduction -- 2 Preliminaries -- 2.1 Differential Operators -- 2.2 The Principal Symbol -- 2.3 Elliptic Operators -- 3 Dirac-Type Operators -- 3.1 Clifford Relations and Dirac-Type Operators -- 3.2 Adapted Operators on the Boundary -- 3.3 Formally Self-adjoint Dirac-Type Operators

4 Boundary Value Problems -- 4.1 Spectral Subspaces -- 4.2 The Maximal Domain -- 4.3 Boundary Conditions -- 4.4 D-Elliptic Boundary Conditions -- 4.5 Self-adjoint D-Elliptic Boundary Conditions -- 4.6 Local and Pseudo-Local Boundary Conditions -- 4.7 Examples -- 5 Spectral Theory -- 5.1 Coercivity at Infinity -- 5.2 Coercivity with Respect to a Boundary Condition -- 6 Index Theory -- 6.1 Fredholm Property and Index Formulas -- 6.2 Relative Index Theory -- 6.3 Boundary Chiralities and Index -- Appendix 1: Dirac Operators in the Sense of Gromov and Lawson

Appendix 2: Proofs of Some Auxiliary Results -- References -- Symplectic and Hyperkähler Implosion -- 1 Introduction -- 2 Symplectic Quivers -- 3 Hyperkähler Quiver Diagrams -- 4 Properties of Hyperkähler Implosion -- 5 Hyperkähler Implosion for Special Orthogonal and Symplectic Groups -- References -- Kazhdan-Lusztig Conjectures and Shadows of Hodge Theory -- 1 Introduction -- 2 Intersection Cohomology and the Decomposition Theorem -- 3 Schubert Varieties and Bott-Samelson Resolutions -- 4 Soergel Modules and Intersection Cohomology -- 5 Soergel Modules for Arbitrary Coxeter Systems

6 The Flag Variety of a Dihedral Group -- 6.1 Gauß's q-Numbers -- 6.2 The Reflection Representation of a Dihedral Group -- 6.3 Schubert Calculus -- References -- Uniform Sup-Norm Bounds on Average for Cusp Forms of Higher Weights -- 1 Introduction -- 1.1 Motivation -- 1.2 Statement of Results -- 1.3 Related Results -- 1.4 Outline of the Paper -- 2 Background Material -- 2.1 Hyperbolic Metric -- 2.2 Cusp Forms of Higher Weights -- 2.3 Maass Forms of Higher Weights -- 2.4 Heat Kernels of Higher Weights -- 2.5 Spectral Expansions -- 3 Heat Kernel Analysis -- 4 Bounds in the Cocompact Setting

5 Bounds in the Cofinite Setting

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