We show that values of finite hypergeometric functions defined over Q correspond to point counting results on explicit varieties defined over finite fields.

Abstract. We show that the big quantum cohomology of the symplectic isotropic Grassmanian IG(2, 6) is generically semisimple, whereas its small quantum cohomology is known to be non-semisimple. This gives yet another case where Dubrovin's conjecture holds and stresses the need to consider the big quantum cohomology in its formulation.

The subject of this paper is the big quantum cohomology rings of symplectic isotropic Grassmannians IG(2, 2n). We show that these rings are regular. In particular, by "generic smoothness", we obtain a conceptual proof of generic semisimplicity of the big quantum cohomology for IG(2, 2n). Further, by a general result of C. Hertling, the regularity of these rings implies that they have a description in terms of isolated hypersurface singularities, which we show in this case to be of type A n−1 . By the homological mirror symmetry conjecture, these results suggest the existence of a very special full exceptional collection in the derived category of coherent sheaves on IG(2, 2n). Such a collection is constructed in the appendix by Alexander Kuznetsov.