Mathematics Colloquium - Yilong Wang
This event is in the past.
Detroit, MI 48202
Speaker: Yilong Wang
Title: Algebraic properties of modular tensor categories
Abstract: Modular tensor categories (MTC) are categorical generalizations of finite abelian groups with non-degenerate quadratic forms. They give rise to invariants of links and 3-manifolds that has similar "quantum" nature as the Jones polynomial. They also provide representations of SL(2, Z/NZ) and mapping class groups of higher genus surfaces which can be viewed as derived from (2+1)-topological quantum field theories (TQFTs) associated to the MTCs.
In this talk, we will introduce the notion of modular tensor categories with an emphsis on its rich connection with representation theory, (2+1)-TQFTs and topological quantum computing. Then we will present our recent work on the algebraic properties of MTCs and the TQFTs associated to them.