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Classification of topological orders

Speaker: Theo Johnson-Freyd

Date: Wed, Jun 9, 2021

Location: Zoom, Online

Conference: CMS Scientific Session on Quantum Mathematics

Subject: Mathematics, Physics, Condensed Matter and Statistical Mechanics, Quantum Physics, Quantum Information, Quantum Computing

Class: Scientific

CRG: Quantum Topology and its Applications

Abstract:

Topological orders have a mathematical axiomatization in terms of their higher fusion categories of extended operators; the characterizing property of these higher fusion categories is that they are satisfy a nondegeneracy condition. After overviewing some of the higher category theory that goes into this axiomatization, I will describe what we do and don't know about the classification of topological orders in various dimensions.