The map that sends a rational curve in a Grassmann variety to its
kernelspan pair can be used to express any (3 point, genus zero)
GromovWitten invariant of a Grassmannian as a classical triple
intersection number of Schubert classes on a twostep flag variety. A
conjecture of Allen Knutson asserts that any such triple intersection
number is equal to the number of triangular puzzles that can be
constructed using a list of puzzle pieces, such that the border of the
puzzles is determined by the intersection problem. I will discuss a
recent proof of this conjecture and how it leads to a positive
combinatorial formula for Grassmannian GromovWitten invariants. I will
also discuss generalizations to equivariant GromovWitten invariants.
This talk is based on papers with A. Kresch, L. Mihalcea, K. Purbhoo,
and H. Tamvakis.
Talk
