BIMSA > BIMSA TQFT and Higher Symmetries Seminar Graphical calculus for anchored planar algebras and tricategories
Graphical calculus for anchored planar algebras and tricategories
Organizers
Ansi Bai , Hank Chen , Liang Kong , Yilong Wang , Zhi-Hao Zhang , Hao Zheng
Speaker
Brett Hungar
Time
Tuesday, November 26, 2024 10:00 AM - 11:45 AM
Venue
A3-2-301
Online
Zoom 468 248 1222 (BIMSA)
Abstract
Anchored planar algebras, a generalized notion of Vaughan Jones' planar algebras, have recently seen use in higher category theory, functional analysis, and TQFT applications. These algebras are equipped with a natural 3-dimensional graphical calculus. We compare this graphical calculus with the 3-dimensional graphical calculus associated to tricategories, and we show that anchored planar algebras can be thought of as living in a particular tricategory. This allows for more general techniques to be applied to anchored planar algebras and expands the types of diagrams that anchored planar algebras can interpret.