Beijing Institute of Mathematical Sciences and Applications

Linzhe Huang , Zhengwei Liu , Sebastien Palcoux , Yilong Wang , Jinsong Wu

Noah Snyder

Wednesday, May 7, 2025 9:30 AM - 11:00 AM

A3-3-301

Zoom 242 742 6089 (BIMSA)

We give a diagrammatic description of the categories of modules coming from the conformal inclusions $(sl(N),N) < (so(N^2-1),1)$. A small variant on this construction has uniform generators and relations which are rational functions in $q = e^{2 \pi i/4N}$, which allows us to construct a new continuous family of tensor categories at non-integer level which interpolate between these categories. This is the second example of such an interpolation category for families of conformal inclusions after Zhengwei Liu's interpolation categories $(sl(N), N + 2) < (sl(N(N+1)/2),1)$ which he constructed using his classification Yang-Baxter planar algebras. Our approach is different from Liu's, we build a two-color skein theory, with one strand coming from $X$ the image of defining representation of $sl(N)$ and the other strand coming from an invertible object g in the category of local modules, and trivalent vertex coming from a map $X (x) X^* \to g$. This is joint work with Cain Edie-Michell.

Reference: https://arxiv.org/abs/2503.13641

He earned a Ph.D. from U.C. Berkeley in 2009 under the supervision of Nicolai Reshetikhin. As an NSF postdoctoral fellow at Columbia University, he was mentored by Dylan Thurston. Since joining Indiana University in January 2013, he advanced to Associate Professor in 2017 and is now Professor. His research focuses on example-driven questions in quantum algebra and quantum topology, with a particular interest in the classification, topology, and arithmetic of fusion categories and subfactors.