Andrew Linshaw (Denver)
Abstract
Vertex algebras are certain noncommutative, nonassociative algebraic structures that arose out of physics in the 1980s. They were first defined mathematically by Borcherds in his proof of the Moonshine Conjecture. In the last 35 years, they have become important in a diverse range of subjects including finite group theory, representation theory, combinatorics, number theory, and geometry. A fruitful perspective is that many vertex algebras can be viewed as quantizations of coordinate rings of arc spaces. In this talk, I will give an introduction to vertex algebras, arc spaces, and their interconnections. This is based on joint work with Bailin Song.