Date: Friday, November 16, 2012
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: The puzzle conjecture for 2step 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 (3point, genus zero) GromovWitten invariants of Grassmannians are special cases of the structure constants of twostep 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 twostep flag varieties that I have recently found a proof of.
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Speaker: Anders Buch
Institution: Rutgers U.
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