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Moonshine - The First Quarter Century and Beyond
Proceedings of a Workshop on the Moonshine Conjectures and Vertex Algebras

$99.99 (C)

Part of London Mathematical Society Lecture Note Series

Peter Bantay, Jan Hendrik Bruinier, Jens Funke, Geoffrey Buhl, Anda Degeratu, Katrin Wendland, Chongying Dong, Zhongping Zhao, Benjamin Doyon, John F. Duncan, Terry Gannon, Elizabeth Jurisich, Haisheng Li, Geoffrey Mason, Atushi Matsuo, Kiyokazu Nagatomo, Akihiro Tsuchiya, Antun Milas, Charles B. Thomas, Michael P. Tuite, Robert A. Wilson
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  • Date Published: September 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521106641

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About the Authors
  • The topic of “Monstrous Moonshine” has been a major development in mathematics since 1979. Beginning with remarkable conjectures relating finite group theory and number theory that stimulated an outpouring of new ideas, “Monstrous Moonshine” deeply involves many different areas of mathematics, as well as string theory and conformal field theory in physics. It has changed the landscape of many fields. This volume consists of 17 papers by research leaders, based on talks presented at a workshop held to mark the anniversary of the “Monstrous Moonshine” conjectures. The papers, which include surveys of many important developments, will give the reader a view of a wide range of current activity and promising directions for future research.

    • Authors include leading experts in the field
    • Highlights possible directions for future research
    • Provides a broad snapshot of current research in the area
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    Product details

    • Date Published: September 2010
    • format: Paperback
    • isbn: 9780521106641
    • length: 416 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.61kg
    • contains: 1 b/w illus.
    • availability: Available
  • Table of Contents

    Preface
    Schedule of talks
    1. Characters of crossed modules and premodular categories Peter Bantay
    2. On the injectivity of the Kudla–Millson lift and surjectivity of the Borcherds lift Jan Hendrik Bruinier and Jens Funke
    3. Ordered spanning sets for vertex operator algebras and their modules Geoffrey Buhl
    4. Friendly giant meets pointlike instantons? On a new conjecture by John McKay Anda Degeratu and Katrin Wendland
    5. Modularity of trace functions in orbifold theory for Z-graded vertex operator superalgebras Chongying Dong and Zhongping Zhao
    6. Twisted modules for vertex operator algebras Benjamin Doyon
    7. Vertex operators and sporadic groups John F. Duncan
    8. The algebraic meaning of being a Hauptmodul Terry Gannon
    9. Borcherds' proof of the Conway–Norton conjecture Elizabeth Jurisich
    10. On the connection of certain Lie algebras with vertex algebras Haisheng Li
    11. Vertex operators and arithmetic: how a single photon illuminates number theory Geoffrey Mason
    12. Rational vertex operator algebras and their orbifolds Geoffrey Mason
    13. Quasi-finite algebras graded by Hamiltonian and vertex operator algebras Atushi Matsuo, Kiyokazu Nagatomo and Akihiro Tsuchiya
    14. On certain automorphic forms associated to rational vertex operator algebras Antun Milas
    15. Moonshine and group cohomology Charles B. Thomas
    16. Monstrous and generalized Moonshine and permutation orbifolds Michael P. Tuite
    17. New computations in the Monster Robert A. Wilson.

  • Editors

    James Lepowsky, Rutgers University, New Jersey
    James Lepowsky is Professor in the Department of Mathematics at Rutgers University, New Jersey.

    John McKay, Concordia University, Montréal
    John McKay is Professor in the Department of Mathematics and Statistics at Concordia University, Montréal.

    Michael P. Tuite, National University of Ireland, Galway
    Michael P. Tuite is a Senior Lecturer in the Department of Applied Mathematics at the National University of Ireland (NUI), Galway.

    Contributors

    Peter Bantay, Jan Hendrik Bruinier, Jens Funke, Geoffrey Buhl, Anda Degeratu, Katrin Wendland, Chongying Dong, Zhongping Zhao, Benjamin Doyon, John F. Duncan, Terry Gannon, Elizabeth Jurisich, Haisheng Li, Geoffrey Mason, Atushi Matsuo, Kiyokazu Nagatomo, Akihiro Tsuchiya, Antun Milas, Charles B. Thomas, Michael P. Tuite, Robert A. Wilson

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