Algebraic Geometry Seminar
Anders Buch
Rutgers University
Quantum K-theory of Grassmannians
Abstract: The Gromov-Witten invariants of a homogeneous space X give the number
of rational curves of fixed degree that meet three general Schubert
varieties, at least when this number is finite. When there are
infinitely many such curves, then the moduli space of (stable)
parametrizations of the curves is a projective variety. The
K-theoretic Gromov-Witten invariants are the Euler characteristic of
such varieties, and were used by Y.-P. Lee and Givental to define a quantum
K-theory ring of X. I will present structure theorems for this ring
when X is a Grassmann variety of type A, and a formula for the
K-theoretic Gromov-Witten invariants that generalizes earlier work
with Kresch and Tamvakis. This is joint work with L. Mihalcea.
Thursday February 21, 2008 at 4:00 PM in SEO 636