PIRSA:25110050

Quantum Groups from Fukaya Categories

Aganagic, M. (2025). Quantum Groups from Fukaya Categories. Perimeter Institute. https://pirsa.org/25110050

Aganagic, Mina. Quantum Groups from Fukaya Categories. Perimeter Institute, Nov. 03, 2025, https://pirsa.org/25110050 

          @misc{ pirsa_PIRSA:25110050,
            doi = {10.48660/25110050},
            url = {https://pirsa.org/25110050},
            author = {Aganagic, Mina},
            keywords = {Mathematical physics},
            language = {en},
            title = {Quantum Groups from Fukaya Categories},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {nov},
            note = {PIRSA:25110050 see, \url{https://pirsa.org}}
          }

Mina Aganagic University of California, Berkeley

Talk numberPIRSA:25110050
DOI10.48660/25110050
Collection
Talk Type Conference
Subject

Abstract

There is a family of Fukaya categories, or categories of A-branes, labeled by a choice of a Lie algebra, which categorify Chern-Simons invariants of links. I will describe how categorified quantum groups emerge from a certain natural set of gluing operations which these Fukaya categories have. This solves a long standing open problem, which is to provide the categorified co-product, providing a monoidal structure for the categorified representations of the quantum group. As a byproduct, this illuminates how quantum group symmetry emerges in Chern-Simons theory.