Claude Sabbah : The quantum cohomology of the Grassmannian as an alternate product of Frobenius manifolds

Posted by , part of the Algebraic Geometry Seminar.

At

April 1, 2008, 4 p.m.

In

SEO 512

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).