Moonshine
Subtitle: the first quarter century and beyond : proceedings of a workshop on the moonshine conjectures and vertex algebras
By: [edited by] James Lepowsky, John McKay, Michael P. Tuite
Series: London mathematical society lecture note series -- 372
Publisher: Cambridge University Press
Published: 2010
Place of publication: New York
Language: eng
ISBN-13: 9780521106641
Description: "In 1979, John Conway and Simon Norton's famous paper, 'Monstrous Moonshine', outlined the remarkable connection between the monster group M and the theory of modular functions. The search for an explanation of this phenomenon involved the development and application of diverse areas of mathematics, including (generalized) Kac-Moody algebras, vertex (operator) algebras, automorphic forms and elliptic cohomology, together with string and conformal field theory from theoretical physics. This volume consists of seventeen papers based on talks presented at a workshop held to mark the anniversary of 'Monstrous Moonshine'. Containing a mixture of expository and current research material, they illustrate its extensive impact and reflect the broad range of research activity that has stemmed from the Moonshine conjectures. Potential directions for future development are also discussed"--Provided by publisher.

"Modular Tensor Categories (MTCs for short)[1, 16] have attracted much attentionin recent years, which is due to the recognition of their importance in bothpure mathematics - 3-dimensional topology, representations of Vertex OperatorAlgebras (VOAs for short) - and theoretical physics"--Provided by publisher.
Table of contents: title: Machine generated contents note: 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.