MS Seminar (Mathematics - String Theory)

Speaker: Sergei Galkin (IPMU)
Title: Apery and Gamma
Date: Thu, Jun 04, 2009, 10:30 - 12:00
Place: Seminar Room at IPMU Prefab. B
Related File: 82.pdf
Abstract: 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.