Mathematical Picture Language Seminar: Yunxiang Ren (Harvard), "Triangular Prism equations and categorification"

Date: 

Tuesday, September 22, 2020, 10:00am

Location: 

Zoom Event: https://harvard.zoom.us/j/779283357

Speaker: Yunxiang Ren
Affiliation: Harvard University
Title : Triangular Prism equations and categorification
Zoom: https://harvard.zoom.us/j/779283357

Abstract:
Fusion categories have been extensively studied by Mathematicians and have proved to have many important applications in quantum physics. A fusion category is completely determined by a set of F-symbols which satisfies the pentagon equations. In general, the fusion categories are constructed by different approaches and their F-symbols remain unknown. In this talk, we introduce the triangular prism equations for fusion categories and show that they are equivalent to the pentagon equations. Moreover, we provide a relevant way to manage the complexity by localization, and thus a possible approach to solve them for the F-symbols. As applications, we provided new criteria for categorification and a categorical approach to the neargroup construction, improving Izumi's equations.

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