Kapustin—Witten TQFT on 3-manifolds and derived skein modules

Abstract: Kapustin and Witten have proposed that there is a 4-dimensional TQFT underlying the geometric Langlands program and have described it as a topological twist of the 4-dimensional maximally supersymmetric Yang—Mills theory. In this talk I will discuss some mathematically-rigorous ways to define the space of states for 3-manifolds, relating it to skein modules and complexified instanton Floer homology of Abouzaid—Manolescu. I will also comment on the possible extension of the geometric Langlands duality to 3-manifolds. This is based on work in progress with D. Jordan and S. Gunningham.

algebraic geometrydifferential geometryquantum algebrasymplectic geometry

Audience: researchers in the topic

Boston University Geometry/Physics Seminar

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