March 24, 2:00 pm
Alexander Postnikov, M.I.T.
"Gromov-Witten invariants and toric tableaux"

Abstract: We present a formula for products of Schubert classes in the quantum
cohomology ring of the Grassmannian. It is given in terms of a generalization
of Schur symmetric polynomials for shapes that are naturally embedded in a
torus. The construction implies symmetries of the Gromov-Witten invariants
(the structure constants of the quantum cohomology) with respect to the action
of S_3, (Z/nZ)^2, and S_2. The last symmetry is a certain "strange duality" of
the GW-invariants that inverts the quantum parameter q. We solve a problem
posed by Fulton and Woodward about characterization of the powers of q that
occur with nonzero coefficients in the quantum product of two Schubert
classes.