Monodromy and K-theory of Schubert Curves via Generalized Jeu de Taquin

Schubert curves are the spaces of solutions to certain one-dimensional Schubert problems involving žags osculating the rational normal curve. e real locus of a Schubert curve is known to be a natural covering space of RP1, 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. e monodromy operator turns out to be the commutator of jeu de taquin rectication 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. is is joint work with Jake Levinson.