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Home » HC & QS - Factorization Homology Seminar: Link factorization homology and quantum knot invariants

Seminar

HC & QS - Factorization Homology Seminar: Link factorization homology and quantum knot invariants March 11, 2020 (10:00 AM PDT - 11:30 AM PDT)
Parent Program:
Location: MSRI: Simons Auditorium
Speaker(s) Owen Gwilliam (University of Massachusetts Amherst)
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1-Gwilliam

Abstract/Media

This talk will be livestreamed.  Join here: https://msri.zoom.us/j/627176824 

This talk will discuss joint work with Kevin Costello and John Francis that connects Feynman diagrams to quantum knot invariants via factorization homology and Koszul duality. A central role is played by an interesting E_3-algebra A_g, which is a formal deformation of C^*(g), the Chevalley cochains of a semi-simple Lie algebra g. This E_3-algebra A_g is Koszul dual to the quantum group U_\hbar(g) in a sense that specializes to the usual Koszul duality between C^*(g) and U(g) when \hbar goes to zero. But this algebra A_g can be constructed by perturbative Chern–Simons theory, as the observables on the Euclidean space R^3. From A_g, together with a finite-dimensional representation of the quantum group, we can construct a link factorization homology theory: the associated knot invariants are equal to the Reshetikhin–Turaev invariants defined by U_\hbar(g). We will discuss facets of these maneuvers.

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1-Gwilliam

H.264 Video 24918_28256_8225_1-Gwilliam.mp4