Mathematics Colloquium - Yilong Wang

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Date: February 17, 2020
Time: 2:45 p.m. - 3:45 p.m.
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Category: Lecture

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.


Department of Mathematics