Topics in the representation theory of vertex operator algebras

Teacher :Robert McRae
Schedule: Every Wed. & Fri. 9:50-11:25 2021-2-22 ~ 5-14
Venue:Conference Room 3, Jin Chun Yuan West Bldg.


The goal is to cover in more depth some of the topics in representation theory of vertex operator algebras that I discussed briefly in my seminar course last semester. Especially, I plan to cover: examples of vertex operator algebras and modules from both rational and logarithmic conformal field theory, intertwining operators and tensor product theory for modules, modular invariance of trace functions, and other topics as time permits.


Some exposure to vertex operator algebras and representation theory of Kac-Moody Lie algebras will be helpful, but not strictly necessary.


Some standard references on vertex operator algebras:
Vertex Operator Algebras and the Monster by Igor Frenkel, James Lepowsky, and Arne Meurman
On axiomatic approaches to vertex operator algebras and modules by Igor Frenkel, Yi-Zhi Huang, and James Lepowsky
Vertex Algebras for Beginners by Victor Kac
Vertex Algebras and Algebraic Curves by David Ben-Zvi and Edward Frenkel
Introduction to Vertex Operator Algebras and Their Representations by James Lepowsky and Haisheng Li
Modular invariance of characters of vertex operator algebras by Yongchang Zhu
Logarithmic tensor category theory for generalized modules for a conformal
vertex algebra by Yi-Zhi Huang, James Lepowsky, and Lin Zhang

Additional course material will be taken from papers to be decided later.