Yi-Zhi Huang
Modular invariance in conformal field theory
Modular invariance plays an important role in the representation theory of infinite-dimensional Lie algebras, the representation theory of vertex operator algebras, conformal field theory and many other areas. This is an introductory course on the modular invariance in conformal field theory, The following topics will be covered in the course:
1. Modular invariance of graded dimensions of suitable modules for Heisenberg algebras, affine Lie algebras and the VIrasoro algebra.
2. Vertex operator algebras, modules and intertwining operators.
3. q-traces and pseudo-traces.
4. Differential equations.
5. Associative algebras and vertex operator algebras.
6. Modular invariance theorem.
7. Applications (Verlinde formula, rigidity of tensor categories of modules for vertex operator algebras and so on).
Lecture notes to be written
Some basic knowledge of first year graduate courses on algebra and complex analysis