Yi-Zhi Huang
Representation theory of vertex operator algebras and two-dimensional conformal field theory
The representation theory of vertex operator algebras is in fact equivalent to two-dimensional chiral conformal field theory. This is an introductory course on the representation theory of vertex operator algebras. In this course I will cover the following topics:
1. Vertex operator algebras, modules and intertwining operators. (I will go through this part quickly if the students know some basic material on vertex operator algebras, for example, from Lepowsky's course in Fall 2021.)
2. Associative algebras and intertwining operators.
3. Convergence, associativity and commutativity of intertwining operators.
4. Tensor products of modules for a vertex operator algebra.
5. Introduction to the tensor category of modules for a vertex operator algebra.
Yi-Zhi Huang: Lecture notes on vertex algebras and quantum vertex algebras (https://sites.math.rutgers.edu/~yzhuang/rci/math/papers/va-lect-notes.pdf). Lecture notes for this course will be written. Before each lecture, notes will be available for the material to be covered in that lecture.
Basic courses in algebra and analysis. I will start from the very beginning of the theory of vertex operator algebras. It will be very helpful if the students know some basic material on vertex operator algebras and modules, for example, from Lepowsky's course in Fall 2021. But these are not required.