Algebraic Geometry Seminar
Claude Sabbah
Ecole Polytechnique, Palaiseau
The quantum cohomology of the Grassmannian as an alternate product of Frobenius manifolds
Abstract: The (big) quantum cohomology of a manifold has the structure of a Frobenius
manifold. If the quantum cohomology of the projective space is well
understood, that of the Grassmannian was only known on its small part. I
will
explain recent results, obtained jointly with I. Ciocan-Fontanine and B.
Kim,
giving a method for obtaining the quantum cohomology of the quotient of a
smooth variety under the action of a reductive group from the quantum
cohomology of the quotient by a maximal torus. For the Grassmannian G(r,n),
this construction can be interpreted as the r-fold alternate product, in the
sense of Frobenius manifolds, of the quantum cohomology of the projective
space P(n).
Tuesday April 1, 2008 at 4:00 PM in SEO 512