University of Sydney Algebra Seminar

Iva Halacheva (University of Melbourne)

Wednesday 24 April, 12-1pm, Place: Carslaw 375

Branching in Schubert calculus and self-dual puzzles

One of the classical questions in Schubert calculus is the expansion of the product in cohomology of two Grassmannian Schubert classes. Knutson and Tao introduced puzzles-combinatorial objects which positively count the coefficients in this expansion. I will describe how self-dual puzzles give the restriction in equivariant cohomology of a Grassmannian Schubert class to the symplectic Grassmannian. 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.