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

doi:10.1017/CBO9780511730054

The theory 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.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-ix
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Schedule of Talks
pp x-xii
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Characters of Crossed Modules and Premodular Categories
pp 1-11
- By Peter Bantay, Institute for Theoretical Physics, Eötvös University, Budapest
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On the Injectivity of the Kudla-Millson Lift and Surjectivity of the Borcherds Lift
pp 12-39
- By Jan Hendrik Bruinier, Mathematisches Institut, Universität zu Köln, Weyertal 86–90, D-50931 Köln, Germany, Jens Funke, Department of Mathematical Sciences, New Mexico State University, P.O.Box 30001, 3MB, Las Cruces, NM 88003, USA
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Ordered Spanning Sets for Vertex Operator Algebras and their Modules
pp 40-54
- By Geoffrey Buhl, Mathematics Department Rutgers University Piscataway, NJ 08854-8019 gbuhl@math.rutgers.edu
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Friendly Giant Meets Pointlike Instantons? On a New Conjecture by John McKay
pp 55-127
- By Anda Degeratu, Dept. of Mathematics, Duke University, Durham NC 27708, USA, Katrin Wendland, Dept. of Mathematics UNC Chapel Hill, Chapel Hill, NC 25599, USA; and Mathematics Institute, University of Warwick CV4-7AL Coventry, UK
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Modularity of Trace Functions in Orbifold Theory for ℤ-Graded Vertex Operator Superalgebras
pp 128-143
- By Chongying Dong, Department of Mathematics University of California, Santa Cruz, CA 95064, Zhongping Zhao, Department of Mathematics University of California, Santa Cruz, CA 95064
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Twisted Modules for Vertex Operator Algebras
pp 144-187
- By Benjamin Doyon, Rudolf Peierls Centre for Theoretical Physics, Oxford University, UK Current address: Department of Mathematical Sciences Durham Unversity, UK
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Vertex Operators and Sporadic Groups
pp 188-203
- By John F. Duncan
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The Algebraic Meaning of Being a Hauptmodul
pp 204-218
- By Terry Gannon, Department of Mathematical Sciences, University of Alberta Edmonton, Canada, T6G 2G1 tgannon@math.ualberta.ca
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Borcherds' Proof of the Conway-Norton Conjecture
pp 219-235
- By Elizabeth Jurisich, Department of Mathematics The College of Charleston Charleston SC 29464 jurisiche@cofc.edu
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On the Connection of Certain Lie Algebras with Vertex Algebras
pp 236-254
- By Haisheng Li, Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102 E-mail address: hli@camden.rutgers.edu
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Vertex Operators and Arithmetic: How a Single Photon Illuminates Number Theory
pp 255-269
- By Geoffrey Mason, Department of Mathematics, UC Santa Cruz
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Rational Vertex Operator Algebras and their Orbifolds
pp 270-281
- By Geoffrey Mason, Department of Mathematics, UC Santa Cruz
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Quasi-finite Algebras Graded by Hamiltonian and Vertex Operator Algebras
pp 282-329
- By Atsushi Matsuo, Kiyokazu Nagatomo, Akihiro Tsuchiya
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On Certain Automorphic Forms Associated to Rational Vertex Operator Algebras
pp 330-357
- By Antun Milas, Department of Mathematics, University at Albany, SUNY Albany, NY 12222 E-mail address: amilas@math.albany.edu
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Moonshine and Group Cohomology
pp 358-377
- By C.B. Thomas
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Monstrous and Generalized Moonshine and Permutation Orbifolds
pp 378-392
- By Michael P. Tuite, Department of Mathematical Physics, National University of Ireland, Galway, Ireland.
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New computations in the Monster
pp 393-403
- By Robert A. Wilson, School of Mathematical Sciences Queen Mary, University of London Mile End Road, London E1 4NS
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Moonshine - The First Quarter Century and Beyond

Proceedings of a Workshop on the Moonshine Conjectures and Vertex Algebras

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-ix

Schedule of Talks
pp x-xii

Characters of Crossed Modules and Premodular Categories
pp 1-11

On the Injectivity of the Kudla-Millson Lift and Surjectivity of the Borcherds Lift
pp 12-39

Ordered Spanning Sets for Vertex Operator Algebras and their Modules
pp 40-54

Friendly Giant Meets Pointlike Instantons? On a New Conjecture by John McKay
pp 55-127

Modularity of Trace Functions in Orbifold Theory for ℤ-Graded Vertex Operator Superalgebras
pp 128-143

Twisted Modules for Vertex Operator Algebras
pp 144-187

Vertex Operators and Sporadic Groups
pp 188-203

The Algebraic Meaning of Being a Hauptmodul
pp 204-218

Borcherds' Proof of the Conway-Norton Conjecture
pp 219-235

On the Connection of Certain Lie Algebras with Vertex Algebras
pp 236-254

Vertex Operators and Arithmetic: How a Single Photon Illuminates Number Theory
pp 255-269

Rational Vertex Operator Algebras and their Orbifolds
pp 270-281

Quasi-finite Algebras Graded by Hamiltonian and Vertex Operator Algebras
pp 282-329

On Certain Automorphic Forms Associated to Rational Vertex Operator Algebras
pp 330-357

Moonshine and Group Cohomology
pp 358-377

Monstrous and Generalized Moonshine and Permutation Orbifolds
pp 378-392

New computations in the Monster
pp 393-403

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Moonshine - The First Quarter Century and Beyond

Proceedings of a Workshop on the Moonshine Conjectures and Vertex Algebras

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