3D mirror symmetry in positive characteristic

Abstract: In positive characteristic, on one hand the quantum D-module (from Gromov--Witten theory) carries extra central endomorphisms known as quantum Steenrod operations. On the other hand, in representation theory, the algebra of differential operators also carry a "large center" in positive characteristic given by a version of the Frobenius map. I will explain how these centers are related to each other by a duality of algebraic symplectic varieties. Joint with Shaoyun Bai.