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Look Inside Recent Advances in Hodge Theory
eBook forthcoming

Recent Advances in Hodge Theory
Period Domains, Algebraic Cycles, and Arithmetic

$91.99 (C)

Part of London Mathematical Society Lecture Note Series

Matt Kerr, Gregory Pearlstein, R. Laza, Z. Zhang, J. Burgos Gil, J. Kramer, U. Kuhn, A. Kaplan, M. Green, P. Griffiths, S. Usui, A. Clingher, C. Doran, A. Harder, A. Novoseltsev, A. Thompson, M. Asakura, R. de Jeu, J. D. Lewis, D. Patel, M. Saito, C. Schnell, S. Abdulali, C. Pedrini, C. Weibel, W. Goldring, S. Patrikis, H. Yoshida, D. Arapura, R. Hain
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  • Date Published: March 2016
  • availability: In stock
  • format: Paperback
  • isbn: 9781107546295

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  • In its simplest form, Hodge theory is the study of periods – integrals of algebraic differential forms which arise in the study of complex geometry and moduli, number theory and physics. Organized around the basic concepts of variations of Hodge structure and period maps, this volume draws together new developments in deformation theory, mirror symmetry, Galois representations, iterated integrals, algebraic cycles and the Hodge conjecture. Its mixture of high-quality expository and research articles make it a useful resource for graduate students and seasoned researchers alike.

    • Discusses recent developments in Hodge theory with a novel focus on period maps
    • Thematic organisation helps the reader see how different topics and techniques fit together
    • High-quality papers from world-leading academics will draw new researchers and young mathematicians to the study of period maps
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    Product details

    • Date Published: March 2016
    • format: Paperback
    • isbn: 9781107546295
    • length: 521 pages
    • dimensions: 228 x 152 x 28 mm
    • weight: 0.73kg
    • contains: 10 b/w illus. 7 tables
    • availability: In stock
  • Table of Contents

    Preface Matt Kerr and Gregory Pearlstein
    Introduction Matt Kerr and Gregory Pearlstein
    List of conference participants
    Part I. Hodge Theory at the Boundary: Part I(A). Period Domains and Their Compactifications: Classical period domains R. Laza and Z. Zhang
    The singularities of the invariant metric on the Jacobi line bundle J. Burgos Gil, J. Kramer and U. Kuhn
    Symmetries of graded polarized mixed Hodge structures A. Kaplan
    Part I(B). Period Maps and Algebraic Geometry: Deformation theory and limiting mixed Hodge structures M. Green and P. Griffiths
    Studies of closed/open mirror symmetry for quintic threefolds through log mixed Hodge theory S. Usui
    The 14th case VHS via K3 fibrations A. Clingher, C. Doran, A. Harder, A. Novoseltsev and A. Thompson
    Part II. Algebraic Cycles and Normal Functions: A simple construction of regulator indecomposable higher Chow cycles in elliptic surfaces M. Asakura
    A relative version of the Beilinson–Hodge conjecture R. de Jeu, J. D. Lewis and D. Patel
    Normal functions and spread of zero locus M. Saito
    Fields of definition of Hodge loci M. Saito and C. Schnell
    Tate twists of Hodge structures arising from abelian varieties S. Abdulali
    Some surfaces of general type for which Bloch's conjecture holds C. Pedrini and C. Weibel
    Part III. The Arithmetic of Periods: Part III(A). Motives, Galois Representations, and Automorphic Forms: An introduction to the Langlands correspondence W. Goldring
    Generalized Kuga–Satake theory and rigid local systems I – the middle convolution S. Patrikis
    On the fundamental periods of a motive H. Yoshida
    Part III(B). Modular Forms and Iterated Integrals: Geometric Hodge structures with prescribed Hodge numbers D. Arapura
    The Hodge–de Rham theory of modular groups R. Hain.

  • Editors

    Matt Kerr, Washington University, St Louis
    Matt Kerr is an Associate Professor of Mathematics at Washington University, St Louis, and an established researcher in Hodge theory and algebraic geometry. His work is supported by an FRG grant from the National Science Foundation. He is also co-author (with M. Green and P. Griffiths) of Mumford-Tate Groups and Domains: Their Geometry and Arithmetic and Hodge Theory, Complex Geometry, and Representation Theory.

    Gregory Pearlstein, Texas A & M University
    Gregory Pearlstein is an Associate Professor of Mathematics at Texas A&M University. He is an established researcher in Hodge theory and algebraic geometry and his work is supported by an FRG grant from the National Science Foundation.

    Contributors

    Matt Kerr, Gregory Pearlstein, R. Laza, Z. Zhang, J. Burgos Gil, J. Kramer, U. Kuhn, A. Kaplan, M. Green, P. Griffiths, S. Usui, A. Clingher, C. Doran, A. Harder, A. Novoseltsev, A. Thompson, M. Asakura, R. de Jeu, J. D. Lewis, D. Patel, M. Saito, C. Schnell, S. Abdulali, C. Pedrini, C. Weibel, W. Goldring, S. Patrikis, H. Yoshida, D. Arapura, R. Hain

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