Monodromy and K-theory of Schubert Curves via Generalized Jeu de TaquinAlgebra & Discrete Mathematics
|Speaker:||Maria Gillespie, UC Berkeley|
|Start time:||Fri, Nov 13 2015, 2:10PM|
Schubert curves are the spaces of solutions to certain one-dimensional Schubert problems involving flags osculating the rational normal curve. The real locus of a Schubert curve is known to be a natural covering space of RP^1, so its real geometry is fully characterized by the monodromy of the cover. It is also possible, using K-theoretic Schubert calculus, to relate the real locus to the overall (complex) Riemann surface.
The monodromy operator turns out to be the commutator of jeu de taquin rectification and promotion on certain skew Young tableaux. We give a new local algorithm for computing this commutator, and use it to provide purely combinatorial proofs of some of the connections to K-theory. If time permits, we will also describe some of the geometric consequences of our combinatorial results. This is joint work with Jake Levinson.