Perverse Schobers and 2-Categorical 3d Mirror Symmetry

Abstract: 3d mirror symmetry predicts an equivalence between 2-categories associated to dual holomorphic symplectic stacks. The first 2-category is of an algebro-geometric flavor and has constructions due to Kapustin/Rozansky/Saulina and Arinkin. The second category depends on symplectic topology and has a conjectural description in terms of the 3d generalized Seiberg-Witten equations (also known as the gauged Fueter equations).

In this talk I will describe joint work with Ben Gammage and Aaron Mazel-Gee proving a variant of 3d mirror symmetry for Gale dual toric cotangent stacks. In particular, we define a combinatorial model for the symplectic 2-category using equivariant perverse schobers. If time permits I will explain work in progress extending our equivalence from toric cotangent stacks to hypertoric varieties. This will provide a categorification of previous results on Koszul duality for hypertoric categories O.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

Free Mathematics Seminar

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