PIRSA:25110050 Conference Mathematical physics

DOI10.48660/25110050

Conference/School: Holomorphic-topological field theories and representation theory

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}}
}

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.

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