对于非紧致的Calabi-Yau 流形，有较为有效的物理和数学计算方法（局部化和拓扑顶点等）。这些方法不适用于紧致的Calabi-Yau 流形，有的不变量的严格数学定义还没有很好地建立，弦理论提供了一个现实有效的途径。本项目将应用和扩展现有的各种物理和数学方法，对于物理唯象方面感兴趣的更一般的紧致Calabi-Yau 流形和D-膜系统: (1)计算开-闭拓扑弦理论的物理超势，运用Quiver 理论研究其相关的规范理论性质； (2)构造其F-理论对偶模型（Calabi-Yau Four-fold背景），以及带有特定规范对称群的对偶杂化弦模型，研究可能的唯像应用； (3)计算这些物理量所包含的几何不变量，如：Ooguri-Vafa 不变量等； (4)与Brane Tiling 有关的Bridgeland 稳定条件及其模空间，真空的相结构和稳定性、以及相变性质。

Some effective methods （localization and topological vertex）for non-compact Calabi-Yau manifold are invalid for compact Calabi-Yau maniford.The string theory provide a effective approach to compute the Ooguri-Vafa invaraints,etc.. By using and extending all available methods from both the physics and mathematics, for generic compact Calabi-Yau threefords and systems of generic D-branes which stringy phenomenology are interested in: (1) computing the superpotentials of the open-closed topological strings,and studying the relevant gauge theory by using the quiver mehtod,etc.； (2) constructing the dual F-theory Calabi-Yau Four-folds and the dual heterotic string model, and probing its application to the stringy phenomenology； (3) studying the geometric invariants relevant to the superpotentials, in particule, the Ooguri-Vafa variants； (4) constructing the moduli space of Bridgeland stability conditions for the Brane Tiling, and studying the relevant properties from physical and mathematical viewponts.