Fall 2026
Yi-Zhi Huang
Subtitle:
Tensor Categories
Course Description:
Tensor categories can be viewed as a natural generalization of rings. They now play an important role in many branches of mathematics and physics, including representation theory, vertex operator algebras, algebraic geometry, algebraic topology, number theory, Von Neumann algebras, quantum field theory, and topological quantum computing, and so on.
This course is an introduction to the theory of tensor categories and tensor categories arising from representation theory and quantum field theory. If there is time, applications of tensor categories to topology will also be briefly discussed.
Here is a list of topics to be covered in the course:
1. Categories and abelian categories.
2. Monoidal categories and tensor categories.
3. Hopf algebras and tensor categories.
4.. Braided tensor categories.
5. Quantum groups, vertex operator algebras and braided tensor categories.
6. Modular tensor categories.
7. Examples of modular tensor categories.
8. Applications of tensor categories.
Text:
1. P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor Categories, Mathematical Surveys and Monographs, Volume 205, American Mathematical Society Providence, Rhode Island, 2015. 2. V. Turaev, Quantum Invariants of Knots and 3-manifolds, de Gruyter Studies in Math., Vol. 18, Walter de Gruyter, Berlin, 1994. 3. Some research and review papers.
Prerequisites:
Some knowledge of first year algebra