CMSA Geometry and Physics Seminar: Kapustin–Witten TFT on 3-manifolds and skein modules
Pavel Safronov - University of Zurich
Kapustin and Witten have studied a one-parameter family of topological twists of 4d N=4 super Yang--Mills. They have shown that the categories of boundary conditions on a 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.