Period integrals, derived categories, and geometries of Moduli spaces

流形是概括平面中的曲线、空间中的曲面等的数学对象。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，卡拉比-丘流形一直吸引着物理学家和数学家的关注。在这项研究中，对 Calabi-Yau 流形的一些几何不变量（称为 Gromov-Witten 不变量）进行了详细的数学研究。特别是，已经揭示了用于计算不变量的某个递归方程中的数学结构。

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.