Date: Friday, January 29, 2016
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: KTheory and Monodromy of Schubert Curves
Abstract: I will describe the combinatorics of Schubert curves, which are onedimensional Schubert problems defined with respect to flags osculating the rational normal curve. The real geometry of such curves is described by orbits of a map \omega on skew tableaux, defined as the commutator of jeu de taquin rectification and promotion. In particular, the real locus of the Schubert curve naturally covers RP^1, with \omega as the monodromy operator.
I will give a local, faster algorithm for computing \omega without rectifying the tableau. Certain steps in the algorithm are in bijection with Pechenik and Yong's 'genomic tableaux', which enumerate the Ktheoretic LittlewoodRichardson coefficient of the Schubert curve. As a corollary, I give purely combinatorial proofs of several numerical results relating the Ktheory and real geometry of the curve. This is joint work with Maria Monks Gillespie.
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Speaker: Jake Levinson
Institution: UM
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