Moonshine - The First Quarter Century and Beyond de James Lepowsky

Moonshine - The First Quarter Century and Beyond: Proceedings of a Workshop on the Moonshine Conjectures and Vertex Algebras: London Mathematical Society Lecture Note Series, cartea 372

James Lepowsky

John McKay

Michael P. Tuite

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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Cuprins

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.