Fusion ring and tensor should be thought of as counterparts of rings in the world of categories. They are ubiquitous in noncommutative algebra and representation theory, and also play an important role in many other areas of mathematics, such as algebraic geometry, algebraic topology, number theory, the theory of operator algebras, mathematical physics, and the theoretical quantum computation. The lecture series will give an introduction to the theory of fusion ring and tensor category. Starting from basic notions, we cover the theory of FP dimension and its applications. Particular emphasis will be put on results that are analogues of results for representation theory of Hopf algebra. The lecture series will not require background knowledge on Hopf algebras.

The lecture series willbegin at 9 in the morning and at 3 in the afternoon of July 9-13. Address: Lecture room38#108.

Schedule

Lecture 1：Fusion ring and and PF-dimension

(speaker:苑呈涛)

Lecture 2: Module over fusion ring module

(speaker:孙华)

Lecture 3：Adjoint based subring and universal grading

(speaker 赵汝菊)

Lecture 4: Complexified fusion rings and weak based rings

(speaker:苑呈涛)

Lecture 5：The casimir matrix of Fusion rings

(speaker : 王志华)

Lecture 6：Represention ring of Hopf algebra

(speaker : 王志华)

Lecture 7：The classification of Fusion category I

(speaker:董井成)

Lecture 8：The classification of Fusion category II

(speaker:董井成)

Lecture 9：Frobenius properties of Hopf algebra and Fusion category

(speaker:董井成)