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From Chern-Simons theory to quantum groups by factorization algebras

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Owen Gwilliam
Tue, 2017-06-06 14:00 - 15:00
MPIM Lecture Hall

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.

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