Mathematical Sciences: Symplectric Topology and It's Applications to String Theory

9401367阮，研究员打算继续他在辛拓扑及其在弦理论中的应用方面的工作。更确切地说，他计划致力于拓扑sigma模型的数学基础-量子上同调理论，使用拓扑sigma模型不变量来研究一般类型的Calabi-Yau流形和曲面，继续研究辛极射线和辛同构，特别是精确辛同构的退化不动点。拓扑性质是研究者研究的对象在小变形情况下保持不变的特殊性质。在过去的一个世纪里，研究数学所有分支中的拓扑性质一直是数学的中心。本课题研究数学物理中的一些拓扑性质，特别是弦理论中的拓扑性质。但这些拓扑性质并不是已知的普通拓扑现象。它们属于一种新的拓扑学--辛拓扑学，研究者认为这将为拓扑学和弦理论提供更好的理解。***

9401367 Ruan The investigator intends to continue his work in the area of symplectic topology and its application to string theory. More precisely, he plans to work on the mathematical foundations of topological sigma model-quantum cohomology theory, to use topological sigma model invariants to study Calabi-Yau manifolds and surfaces of general type, to continue to work on symplectic extremal rays and symplectomophisms, in particular, degenerate fixed points of exact symplectomorphisms. Topological properties are special properties that remain unchanged under the small deformation of objects that the investigator studies. Studying topological properties in all branches of mathematics has been in the center of mathematics for the past century. This project studies some topological properties arising from mathematical physics, in particular, from string theory. But those topological properties are not ordinary topological phenomenon known before. They belong to a new kind of topological theory-Symplectic topology, which the investigator believes will provide much better understanding both for topology theory and for string theory. ***