Peng Zhou: Cutting-and-gluing in categorified representation theory

Khovanov-Lauda and Rouquier initiated the higher representation program, by categorifying (the negative part) U_q(g)^- to a monoidal category U. In this talk, I will first give a symplectic geometric realization of this monoidal category(https://arxiv.org/abs/2406.04258), then explain how to take tensor product of two monoidal module categories by study a 'disk with three stops'. This is work in progress joint with  Mina Aganagic, Elise LePage, Vivek Shende.