Quantum cohomology of isotropic Grassmannians
-- Anders Skovsted Buch, January 28, 2005

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The (small) quantum cohomology ring of a homogeneous space is a
deformation of the classical cohomology ring, which uses the three
point, genus zero Gromov-Witten invariants as its structure constants.
I will present structure theorems for the quantum cohomology of
isotropic Grassmannians, including a quantum Pieri rule for
multiplication with the special Schubert classes, and a presentation
of the quantum ring over the integers with the special Schubert
classes as the generators.  These results are new even for the
ordinary cohomology of isotropic Grassmannians, and are proved
directly from the definition of Gromov-Witten invariants by applying
classical Schubert calculus to the kernel and span of a curve.  This
is joint work with A. Kresch and H. Tamvakis.