## MS Seminar (Mathematics - String Theory)

Speaker: | Sergei Galkin (IPMU) |
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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. |