In mathematics, Chern-Simons theory determines link invariants in two distinct ways: via quantum groups and via Feynman diagrammatics. This talk aims to explain how these approaches are related, using a more general story about factorization algebras and quantum field theory. As I will explain, the observables of perturbative Chern-Simons theory naturally form an algebra over the little 3-disks operad, and so line operators form a braided monoidal category. Higher abstract nonsense, notably Koszul duality, lets us recover a quantum group with formal parameter. This work in progress is joint with K. Costello and J. Francis.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/5312