Speaker: Sergey Galkin

Title: Apery and Gamma

Date: Jun 04, 2009, 10:30 - 12:00

Place: IPMU, Seminar Room at Prefab. B

For a Fano variety X we introduce the Apery class - characteristic cohomology class derived from quantum D-module of X. Experimentally it's coefficients with respect to an integer Betti basis are shown to be polynomials evaluated in the values of Riemann's zeta-function of positive integer arguments.
This structure resembles the Gamma-class of Fano varieties, that conjecturally provides the integral structure of quantum cohomology coming from the integral Betti structure in the fiber of the mirror partner. We find a relation between Apery class and Gamma class, and give a physical (i.e. modulo Mirror Symmetries conjectures) explanation why this relation holds.