|Date: Friday, November 16, 2012
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: The puzzle conjecture for 2-step flag manifolds
Abstract: A conjecture of Allen Knutson from 1999 asserts that the Schubert structure constants of the cohomology ring of any flag variety SL(n)/P are equal to the number of triangular puzzles with specified border labels that can be constructed using a list of puzzle pieces. Knutson quickly found a counterexample to the general conjecture. Joint work of myself, Kresch, and Tamvakis later showed that the (3-point, genus zero) Gromov-Witten invariants of Grassmannians are special cases of the structure constants of two-step flag varieties, and we suggested that Knutson's conjecture might be true in this special case, backed up by computer verification for n <= 16. I will speak about a proof of this conjecture, joint with Andrew Kresch, Kevin Purbhoo, and Tamvakis. I will also explain a generalization to the equivariant structure constants of two-step flag varieties that I have recently found a proof of.
Speaker: Anders Buch
Institution: Rutgers U.