Abelian 3d mirror symmetry

Abstract: 3d mirror symmetry is a proposed physical duality relating a pair of 3d N=4 field theories. Various mathematical shadows of this result have been studied, but ultimately (after a topological twisting), 3dMS should entail an equivalence between a pair of 2-categories associated to the algebraic (respectively, symplectic) geometry of a pair of holomorphic symplectic stacks. In general, the definitions of these 2-categories are not known, but in this talk we explain how one can define the relevant 2-categories and construct an equivalence between them in the case where the spaces involved are linear quotients by a torus. Potential applications include a Betti geometric version of Tate's thesis and a recovery of earlier results on Koszul duality for hypertoric categories O. This is joint work with Justin Hilburn and Aaron Mazel-Gee.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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