(UC Santa Cruz)
Abstract: Vertex operator algebras are a new class of algebraic structures which have recently arisen in mathematics and physics. Monstrous moonshine is about the connection between the monster simple group and modular functions. In this talk I will review the history of monstrous moonshine, including the basic facts about vertex operator algebra and Borcherds' proof of Conway-Norton's moonshine conjecture. I will also discuss Norton's generalized moonshine conjecture and its relation with orbitfold conformal field theory.