Quantum cohomology of the symplectic Grassmannians

Abstract.

Odd symplectic Grassmannians are the Grassmannians of isotropic subspaces of an odd-dimensional ambient vector space endowed with an antisymmetric form of maximal rank. They are endowed with an action of a non-reductive group, the odd symplectic group, with only two orbits. As a result these spaces, despite being non-homogeneous, behave in many ways like the usual symplectic Grassmannians.

In this talk I will explain how to study the classical and quantum cohomology of these spaces, starting with a description of some of their moduli spaces of stable maps. In the special case of odd symplectic Grassmannian I obtain a full description of the quantum cohomology. This enables me to check for these examples a conjecture by Dubrovin relating properties of the quantum cohomology of a Fano variety with properties of their quantum cohomology.