Mathematical Sciences: Symplectic Topology and Its Applications to String Theory

9703870阮这个项目是关于卡勒几何及其在镜面对称性方面的应用。更具体地说，研究者将使用Kahler或Riemannian塌陷的想法--考虑一系列Kahler流形及其极限流形--来加深我们对镜像对称性的理解。黎曼流形是带有距离概念的弯曲空间，也称为度量。(紧)黎曼流形的整体本身可以被赋予一个度量，这样当给定这样的流形的无限集合时，谈论聚集或收敛是有意义的。镜像对称是物理学家最先发现的一种现象：在流行的10维弦理论宇宙模型中，不可见的6维出现了，即所谓的具有一定对称性的Calabi-Yau流形。

9703870 Ruan This project lies in the area of Kahler geometry and its application to mirror symmetry. More specifically, the investigator is to use the idea of Kahler or Riemannian collapsing - a sequence of Kahler manifolds and their limit manifold are considered - to further our understanding of mirror symmetry. Riemannian manifolds are curved spaces equipped with a notion of distance, also called a metric. The totality of (compact) Riemannian manifolds itself can be given a metric so that when given an infinite collection of such manifolds it makes sense to talk about clustering or converging. Mirror symmetry is a phenomenon first discovered by physicists: in the popular 10-dimensional string theory model of the universe, the invisible 6-dimensions arise as so called Calabi-Yau manifolds possessing certain symmetry.