|Speaker:||Sergei Galkin (IPMU)|
|Title:||Apery and Gamma|
|Date:||Thu, Jun 04, 2009, 10:30 - 12:00|
|Place:||Seminar Room at IPMU 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.