Arithmetic of Calabi-Yau Manifolds
主 题: Arithmetic of Calabi-Yau Manifolds
报告人: Professor Philip Candelas (Oxford University)
时 间: 2015-09-18 15:00 - 16:00
地 点: 理科一号楼 1114（数学所活动）
Calabi-Yau manifolds have many remarkable properties owing to their relation to supersymmetry and string theory. I will give a review of the arithmetic of these manifolds, from the perspective of a physicist. The main quantities of interest in the arithmetic context are the numbers, N_r(\psi), of points of the manifold considered as a manifold over the field with $p^r$ elements. We shall be concerned with the computation of these numbers and their dependence on the parameters, collectively denoted by \psi. The first surprise, for a physicist, is that the N_r(\ps) are given by expressions that involve the periods of the manifold. I will review also recent computations of the \zeta function for certain one-parameter families of manifolds and comment on the appearance of modular functions.
