From Chern-Simons theory to quantum groups by factorization algebras

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.