Hodge Theory, Complex Geometry, and Representation Theory.

Intro -- EDITORIAL COMMITTEE -- Contents -- Preface -- Conference Attendees -- Conference Speakers -- The smooth center of the cohomology of a singular variety -- 1. Definition and properties of the smooth center of the cohomology -- 2. H1sm(C) of a singular curve -- 3. A simple strange surface -- 4. Revisiting the example of Barbieri-Viale and Srinivas -- 5. Examples of varieties with normal crossings -- 6. More on varieties with normal crossings -- References -- Developments in Noether-Lefschetz theory -- Introduction -- 1. The classical theorem -- 2. New ideas: the infinitesimal approach -- 3. Components of the Noether-Lefschetz locus -- 4. Class groups and Noether's theorem -- References -- Compact quotients of non-classical domains are not K¨ahler -- Introduction -- 1. Compact Subvarieties -- 2. Harmonic and Pluriharmonic Maps -- 3. Proof of Theorem 0.1 -- References -- Algebraicity of Hodge loci for variations of Hodge structure -- 1. Introduction -- 2. Results, consequences and generalizations -- 3. Reduction to a Local Statement -- 4. Splittings of MHS and Asymptotics of Period Maps -- 5. The Local Statement: One variable case -- 6. The Local Statement: Bivariate Case -- References -- On the differential equations satisfied by certain Harish-Chandra modules -- 1. Introduction -- 2. Notations and preliminaries -- 3. The three filtrations -- 4. The spectral sequences associated to the filtrations -- 5. The spectral sequence associated to the filtration -- 6. The spectral sequence associated to the filtration -- 7. Involutivity and the characteristic module of the PDE associated to -- 8. The characteristic variety -- Appendix A. The symbol spectral sequence and higher characteristic varieties -- References -- Kato-Usui partial compactifications over the toroidal compactifications of Siegel spaces -- 1. Introduction.

2. Construction of fans and their boundary component structures -- References -- Notes on the representation theory of ₂(ℝ) -- Introduction -- 1. Irreducible representations of ₂ -- 2. Parabolic induction -- 3. Eisenstein series -- 4. Modular forms -- 5. Cuspidal automorphic forms -- 6. Cohomology -- 7. Appendix I: ²( ) and the { _{ }^{±}} -- 8. Appendix II: Poincaré series -- References -- Cup products in automorphic cohomology: The case of ₄ -- 1. Introduction -- 2. Review of Mumford-Tate groups and domains -- 3. Cohomology and automorphic cohomology -- 4. Penrose transforms and arithmeticity -- 5. Cup products and TDLDS -- 6. Proof of Theorem 5.4 -- References -- Hodge type conjectures and the Bloch-Kato theorem -- 1. Introduction -- 2. Notation -- 3. Cycle class maps -- 4. Key example I -- 5. Beilinson-Hodge conjectures -- 6. Galois actions -- 7. Integral formulations and the Milnor regulator -- 8. Rigidity revisited -- 9. Bloch-Kato theorem and its consequences -- References -- Principal Hodge representations -- 1. Introduction -- 2. Hodge representations -- 3. Symplectic Hodge groups -- 4. Orthogonal Hodge groups -- 5. Exceptional groups -- 6. Special linear Hodge groups -- References -- A study of mirror symmetry through log mixed Hodge theory -- Contents -- 0. Introduction -- 1. Log mixed Hodge theory -- 2. Examples -- 3. Quintic threefolds -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.