Moonshine - The First Quarter Century and

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.

Preface	p. vii
Schedule of Talks	p. x
Characters of Crossed Modules and Premodular Categories	p. 1
On the Injectivity of the Kudla-Millson Lift and Surjectivity of the Borcherds Lift	p. 12
Ordered Spanning Sets for Vertex Operator Algebras and their Modules	p. 40
Friendly Giant Meets Pointlike Instantons? On a New Conjecture	p. 55
Modularity of Trace Functions in Orbifold Theory for Z-Graded Vertex Operator Superalgebras	p. 128
Twisted Modules for Vertex Operator Algebras	p. 144
Vertex Operators and Sporadic Groups	p. 188
The Algebraic Meaning of Being a Hauptmodul	p. 204
Borcherds' Proof of the Conway-Norton Conjecture	p. 219
On the Connection of Certain Lie Algebras with Vertex Algebras	p. 236
Vertex Operators and Arithmetic: How a Single Photon Illuminates Number Theory	p. 255
Rational Vertex Operator Algebras and their Orbifolds	p. 270
Quasi-finite Algebras Graded by Hamiltonian and Vertex Operator Algebras	p. 282
On Certain Automorphic Forms Associated to Rational Vertex Operator Algebras	p. 330
Moonshine and Group Cohomology	p. 358
Monstrous and Generalized Moonshine and Permutation Orbifolds	p. 378
New computations in the Monster	p. 393
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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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