BIMSA > BIMSA-Tsinghua Quantum Symmetry Seminar BIMSA-Tsinghua Quantum Symmetry Seminar Planar algebras associated to cocommuting squares
Planar algebras associated to cocommuting squares
Organizers
Linzhe Huang , Zhengwei Liu , Shuang Ming , Sebastien Palcoux , Yilong Wang , Jinsong Wu
Speaker
Junhwi Lim
Time
Wednesday, November 19, 2025 10:30 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089 (BIMSA)
Abstract
The ‘generalized symmetries’ of subfactors are encoded by their planar algebras. A natural foundational question is “What minimal structure can be universally expected from these symmetries?” For arbitrary subfactors, Jones showed that the associated planar algebra contains the Temperley-Lieb-Jones algebra. When an intermediate subfactor is present, the planar algebra contains the Fuss-Catalan-Bisch-Jones algebra, introduced by Bisch and Jones. However, the situation with two intermediate subfactors remains an open problem. As a natural special case, we study cocommuting squares of factors with ‘group-like’ properties. We exhibit the skein relations of their associated planar algebras and show that these algebras extend the partition algebras. This is based on a joint work with Dietmar Bisch.
Speaker Intro
Junhwi Lim is a Ph.D. student in Mathematics at Vanderbilt University, where he has been studying under the supervision of Prof. Dietmar Bisch since 2021. His research focuses on subfactors and their connections to combinatorics, tensor categories, functional analysis, and mathematical physics.