The University of Michigan Combinatorics Seminar


Abstract 

The (small) quantum cohomology ring of a Grassmann variety encodes the
enumerative geometry of rational curves in this variety. By using
degeneracy loci formulas on quot schemes, Bertram has proved quantum
Pieri and Giambelli formulas which give a complete description of the
quantum cohomology ring. In this talk I will present elementary new
proofs of these results which rely only on the definition of
GromovWitten invariants and standard facts about the usual cohomology
of Grassmannians. I will also report on work in progress with Andrew
Kresch and Harry Tamvakis towards obtaining a quantum
LittlewoodRichardson rule for the genus zero GromovWitten invariants
on Grassmannians.
