Quantum Steenrod Operations, p-curvature, and Representation Theory

Quantum Steenrod operations are deformations of classical Steenrod operations on mod p cohomology defined by counts of genus 0 holomorphic curves with a p-fold symmetry, for a prime p. We explain their relationship with the p-curvature of the quantum connection, and survey recent developments. This relationship was first noticed through the study of quantum Steenrod operations of symplectic resolutions, a rich class of smooth symplectic manifolds arising from representation theory. We describe the role of quantum Steenrod operations in the 3D mirror symmetry program, which concerns a duality between such symplectic resolutions. Partly joint with Shaoyun Bai.