Abstract: 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.