Beyond Moonshine

11/25/2008 - 12:15pm
11/25/2008 - 1:10pm
Geoffrey Buhl (California State University Channel Island)

Mathematically, "Moonshine" refers to the unexpected relationship between the largest sporadic simple group, the Monster, and the modular function, j. One of the products of the study and proof of the Moonshine conjectures are new algebraic objects called vertex operator algebras. Surprisingly, these objects are exactly the so-called chiral algebras of string theory. For certain vertex operator algebras, there is an associated modular function, generalizing one aspect of the moonshine conjectures. In this talk I will describe the moonshine conjectures, give a definition of vertex operator algebras, and describe which vertex operator algebras have modularity properties.

ML 211

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