Geometry & Physics Seminar

3d mirror symmetry, also known as symplectic duality, is a duality originated from physics between the so-called Higgs branch and Coulomb branch of 3d supersymmetric gauge theories. In this talk, I will discuss the exposition of this duality in the case of the cotangent bundle of Grassmannians, for certain geometric invariants called elliptic stable envelopes, introduced by Aganagic-Okounkov. The restriction matrix to fixed points of elliptic stable envelopes for T^*Gr and its mirror turn out to be related to each other under transposition and an exchange of equivariant and K\"ahler parameters. In terms of explicit formulas, the duality gives rise to infinitely many nontrivial identities of theta functions. This work is joint with R. Rim\'anyi, A. Smirnov and A. Varchenko. Speaker(s): Zijun Zhou (Stanford)