Abstract: Puzzles in Schubert calculus were originally developed by A. Knutson and T. Tao as combinatorial objects for computing the expansion of the product of two Grassmannian Schubert classes. I will describe how self-dual puzzles in turn allow us to compute the restriction of a Grassmannian Schubert class to the symplectic Grassmannian in equivariant cohomology. The proof uses the machinery of quantum integrable systems. Time permitting, I will also discuss some ideas about how to interpret and generalize this result using Lagrangian correspondences and Maulik-Okounkov stable classes. This is joint work in progress with Allen Knutson and Paul Zinn-Justin.