Algebra and Combinatorics Seminar

Date: February 1, 2019

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Qing Zhang, TAMU

Title: Classification of Super-modular Categories

Abstract: I will explain the connection between topological quantum computing and tensor categories. The most promising proposal for topological quantum computation is anyon braiding in 2D topological phases of matter. The algebraic theory of 2D topological phases corresponds to tensor category theory in a very precise way. I will focus on super-modular categories, a type of tensor category related to fermionic topological phases similarly to the way that modular categories are related to bosonic phases.

Super-modular categories are interesting from a purely mathematical standpoint as well. For example, any unitary pre-modular category is the equivariantization of a modular or super-modular category. In this talk, I will discuss a number of properties of super-modular categories parallel to those of modular categories. Time permitting, I will also discuss the classification of super-modular categories of rank 8.