Colloquium
4:00 p.m., Monday (January 24, 2005)
MATH 203
Anders Buch
Aarhus Universitet
Quantum cohomology of Grassmannians
The (small) quantum cohomology ring of a Grassmann variety is a deformation
of the usual cohomology, which encodes the threepoint, genus zero GromovWitten
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 GromovWitten invariants, using only
elementary facts from Schubert calculus. I will also discuss some known and
conjectured formulas for GromovWitten invariants.
Refreshments will be served at 3:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).
