Mathematical Physics Seminar: Safronov (Edinburgh)

Mathematical Physics Seminar, external speaker:

Pavel Safronov (University of Edinburgh)

Title: Kapustin–Witten TFT on 3-manifolds and skein modules

Abstract: Kapustin and Witten have studied a one-parameter family of topological twists of the 4d N=4 super Yang–Mills theory. They have shown that the categories of boundary conditions on the surface are exactly the categories participating in the geometric Langlands program of Beilinson and Drinfeld. Moreover, S-duality is manifested as a quantum geometric Langlands duality after the topological twist. In this talk I will describe some mathematical formalizations of Hilbert spaces of states on a 3-manifold. I will outline an equivalence between two such possible formalizations: complexified Floer homology of Abouzaid--Manolescu and skein modules. This is a report on work in progress joint with Sam Gunningham.

1 h talk, followed by informal discussion.

All are welcome!