Séminaire Algèbre Géométrie Algébrique Topologie Algébrique :

Le 12 mai 2011 à 11:15 - salle 431

Présentée par Iritani Hiroshi - Kyoto University

Quantum cohomology and Periods

Quantum cohomology is a deformation of the cup product of cohomology ring defined by Gromov-Witten invariants (i.e. number of holomorphic spheres in a given manifold). Mirror symmetry predicts a certain relationship between quantum cohomology and periods of the mirror, namely, periods are solutions to the "quantum differential equation" defined by quantum cohomology. In this talk, I will make precise what solutions of the quantum differential equation corresponds to periods. This makes quantum cohomology of Calabi-Yau hypersurfaces a polarized variation of Z-Hodge structure.