Course: Vertex Operator Algebras and Conformal Field Theory
Times: T 12:30pm - 1:45pm DBRT 308. TH 2:00 - 3:15 DBRT 326.
Recommended Text 1:  Introduction to Vertex Operator Algebras and Their Representations,  James Lepowsky and Haisheng Li,  Birkhauser, Progress in Mathematics, 227, 2004.
Recommended Text 2:  Two-Dimensional Conformal Geometry and Vertex Operator Algebras, Yi-Zhi Huang,  Birkhauser, Progress in Mathematics, 148, 1997.
Instructor:  Professor Katrina Barron
Office:  106 Hayes-Healy Center
Phone:  631-3981
Email:  kbarron@nd.edu
Office Hours:  TBA

Course Description:   This will be an introduction to vertex operator algebras including basic examples.  Vertex operator algebras arise as fundamental objects in both physics and mathematics.  In mathematics, they arise naturally in the representation theory of infinite-dimensional Lie algebras and the Monster finite simple group; in physics, vertex operator algebras arise as the basic building blocks of conformal field theory.  Conformal field theory (or more specifically, string theory) and related superconformal theories are the most promising attempts at developing a physical theory that combines all fundamental interactions of particles, including gravity.

Vertex operator algebra theory is extremely rich with important ties to number theory, the representation theory of infinite-dimensional Lie algebras and finite simple groups, conformal geometry, and topology.  Besides giving an introduction to vertex operator algebras (VOAs), the course will cover aspects of the geometric interpretation of VOAs in terms of the conformal geometry of propagating strings.  Time permitting, we may also cover such topics as vertex operator superalgebras (which arise physically in superstring theory), modules (representations) for VOAs, tensor product theory for VOAs, and recent results on modular tensor categories which allow for the construction, in a rigorous mathematical sense, of a significant portion of conformal field theory.

I will be assuming a basic knowledge of some algebra and complex analysis.