Puzzles in Schubert calculus were originally developed by Knutson and
Tao as combinatorial objects for computing the expansion of the
product of two Grassmannian Schubert classes. I will present a puzzle
rule for restricting type A Schubert classes for the Grassmannian to
type C in equivariant cohomology. The proof uses the machinery of
quantum integrable systems. I will then describe work in progress
toward an extension of this rule to cotangent bundles in the context
of Lagrangian correspondences between symplectic resolutions, and
Maulik—Okounkov classes. This joint work with A. Knutson and P.
Zinn-Justin.