Combinatorics of 3d Mirror Symmetry

Abstract: 3d mirror symmetry is a conjectured duality among symplectic varieties that expects deep relationships between enumerative invariants of varieties that may appear to be unrelated. In this talk, I will describe the general setup of 3d mirror symmetry and will then explain its nontrivial combinatorial implications in the example of the cotangent bundle of the Grassmannian and its mirror variety. In this case, the 3d mirror relationship is governed by a new family of difference operators which characterize the Macdonald polynomials.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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