Colloquium abstracts

Vijay Ravikumar
TIFR
February 13, 2014

Triple Intersection Formulas for Isotropic Grassmannians:  A K-theoretic Pieri formula provides a convenient way to calculate the product of arbitrary Schubert classes with certain special classes in the Grothendieck ring of a homogeneous space. In this talk we calculate the K-theoretic triple intersection numbers of Pieri type, for Grassmannians of types B, C, and D. These can be used to quickly compute K-theoretic Pieri coefficients, which are alternating sums of triple intersection numbers. Our method generalizes a geometric argument used by Hodge to prove the classical Pieri rule, and requires us to examine the projected Richardson varieties in the underlying projective space of the Grassmannian. The equations defining these projected Richardson varieties have applications outside of K-theory as well. Time permitting, we will discuss their use in studying the equivariant cohomology of Grassmannians of types B, C, and D.