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Topics in Representation Theory
Topics in Representation Theory
Towards $\hat{Z}$ from infinite-dimensional representations of $U_q(sl_2)$
Towards $\hat{Z}$ from infinite-dimensional representations of $U_q(sl_2)$
Organizers
Speaker
Time
Friday, September 4, 2026 1:00 PM - 2:30 PM
Venue
A3-2a-302
Online
Zoom 361 038 6975
(BIMSA)
Abstract
The shadow world is a graphical calculus for quantum \(6j\)-symbols of finite-dimensional representations of \(U_q(sl_2)\). It provides a model for the colored Jones polynomial, which is equivalent to the model coming from the R-matrix. The R-matrix statsum for Verma modules of \(U_q(sl_2)\) can reproduce Gukov-Manolescu series. This talk is devoted to the study of Gukov-Manolescu series from the perspective of the shadow world, which gives hints on a possible target category for the Reshetikhin-Turaev functor.
Speaker Intro
I was a PhD student in Mathematics at Tsinghua University, Beijing, China; under supervision of Prof. Nicolai Reshetikhin. My research focuses on the interplay between representation theory of quantum groups, TQFTs and mathematical physics.