MIT Combinatorics Seminar

Tableaux combinatorics of affine Schubert calculus

Jennifer Morse  (University of Miami)

Friday, May 04, 2007    4:15 pm    Room 2-136


A family of symmetric polynomials arose in our study of an open problem regarding tableaux and Macdonald polynomials. We will discuss this problem and see how it led us to explicit combinatorial rules for calculating in both the homology and cohomology of the affine Grassmannian. Our results suggest an 'affine' tableaux approach to the Macdonald problem as well as enumerative geometric questions concerning certain Gromov-Witten invariants.

No background in Macdonald polynomials, geometry or Schubert calculus will be assumed.

Joint work with Lapointe and with Lam, Lapointe, and Shimozono