4:00 p.m., Monday (January 24, 2005)
Quantum cohomology of Grassmannians
The (small) quantum cohomology ring of a Grassmann variety is a deformation
of the usual cohomology, which encodes the three-point, genus zero Gromov-Witten
invariants as its structure constants. By using degeneracy loci formulas on
quot schemes, Bertram has proved quantum Pieri and Giambelli formulas, which
give a combinatorial description of the quantum ring. I will explain how my
definition of a kernel and span of a curve makes it possible to derive these
results directly from the definition of Gromov-Witten invariants, using only
elementary facts from Schubert calculus. I will also discuss some known and
conjectured formulas for Gromov-Witten invariants.
Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).