Period integrals, derived categories, and geometries of Moduli spaces

流形是数学对象，它概括了平面中的曲线，空间中的曲面等。在现代物理学中，流形被用作宇宙的数学模型。在过去的二十年里，Calabi-Yau流形一直吸引着物理学家和数学家的注意力。本文对Calabi-Yau流形的一些几何不变量进行了详细的数学研究，这些几何不变量被称为Gromov-Witten不变量。特别是在一定的递归方程计算的不变量的数学结构已被揭示。

Manifolds are mathematical objects which generalize curves in a plane, surfaces in a space, etc. In modern physics, manifolds are used as a mathematical model of the universe. Over the last two decades, Calabi-Yau manifolds have been attracting attentions of both physicists and mathematicians. In this research, a detailed mathematical study has been done on some geometric invariants, called Gromov-Witten invariants, of Calabi-Yau manifolds. In particular mathematical structures in a certain recursive equation for computing the invariants have been revealed.