Quantum cohomology and period

Mirror symmetry conjecture says that one can calculate
the number of rational curves (Gromov-Witten invariants) in terms
the period of the mirror. This has been proved in many cases including
complete intersections in toric varieties. The Gromov-Witten invariants
here define a deformation of the cup product of the cohomology ring
which is called quantum cohomology. In this talk, I will describe a precise
relationship between quantum cohomology and integral periods of the mirror.
This introduces a polarized Z-Hodge structure in quantum cohomology
of Calabi-Yau hypersurfaces.