- Series
- Progress in Mathematics, Volume 319
- Publisher
- Cham, Switzerland : Birkhauser/Springer International Publishing, [2016]
- Subject
- Geometry, AlgebraicGeometry, DifferentialMathematiciansOperator theoryTopology
- Format
- Web
- ISBN
- 33194364819783319436487

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Electronic resource |

- Description
- 1 online resource (427 pages).
- Additional Authors
- Ballmann, Werner,Hirzebruch, Friedrich,
- Notes
- "The Arbeitstagung 2013 was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. This volume contains contributions from speakers and participants, covering a variety of topics from algebraic geometry, topology, differential geometry, operator theory, and representation theory."--Title page verso.3.1 The Statement of the Correspondence3.2 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 Properties of Hyperkähler Implosion5 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.4.4 D-Elliptic Boundary Conditions4.5 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.Fivebranes and 4-Manifolds.Includes bibliographical references.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).This volume contains selected papers authored by speakers and participants of the 2013 Arbeitstagung, held at the Max Planck Institute for Mathematics in Bonn, Germany, from May 22-28. The 2013 meeting (and this resulting proceedings) was dedicated to the memory of Friedrich Hirzebruch, who passed away on May 27, 2012. Hirzebruch organized the first Arbeitstagung in 1957 with a unique concept that would become its most distinctive feature: the program was not determined beforehand by the organizers, but during the meeting by all participants in an open discussion. This ensured that the talks would be on the latest developments in mathematics and that many important results were presented at the conference for the first time. Written by leading mathematicians, the papers in this volume cover various topics from algebraic geometry, topology, analysis, operator theory, and representation theory and display the breadth and depth of pure mathematics that has always been characteristic of the Arbeitstagung.Uniform Sup-Norm Bounds on Average for Cusp Forms of Higher Weights1 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; 6 Bounds for Covers; 7 Optimality of the Bounds; 7.1 Optimality in the Cocompact Setting; 7.2 Optimality in the Cofinite Setting; References.