Introduction to Vertex Algebras and Their Representation Theory

Fei Qi (University of Manitoba)

Jan 1, 2021 — Jun 1, 2021

About the course

Vertex algebras are algebraic structures formed by the vertex operators that appear both in mathematics and in physics. In mathematics, vertex algebras are used to study the Monster group, the largest finite simple group. The representation theory of vertex algebras gives a mathematical construction to two-dimensional conformal field theories. In this course, we will take an axiomatic approach and focus on the definition, axioms, properties and examples. If time permits, we will also introduce the theory of vertex tensor categories associated to the modules for the vertex operator algebras.


This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

Enrollment Details

Course Name
Introduction to Vertex Algebras and Their Representation Theory
Jan 1, 2021 — Jun 1, 2021
Course Number
MATH 8510
Section Number
Section Code


For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website

Other Course Details

Reference texts

  1. Lepowsky-Li, Introduction to vertex algebras and its representation theory
  2. Vertex Operator Algebras and the Monster by Igor Frenkel, James Lepowsky, and Arne Meurman
  3. A series of papers by Yi-Zhi Huang, Jim Lepowsky and Lin Zhang on intertwining operators and vertex tensor categories.