Algebra Seminar: Halacheva -- Branching in Schubert calculus and self-dual puzzles

Iva Halacheva (University of Melbourne) 

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

Title: Branching in Schubert calculus and self-dual puzzles 

Abstract: 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.