Mathematical Sciences: Geometry of Surfaces, Soliton Equations, and Loop Groups

首席研究员将继续研究 常平均曲率空间中的极小曲面在 特别是他将研究表面的高等属，如 镶嵌在球体中的环面。将使用的技术包括 无限维空间中的可积系统这种技术 与研究这些的标准方法有很大的不同 到目前为止的问题。 该奖项将支持一般领域的研究， 微分几何和全局分析。微分几何 是研究空间的几何形状 和空间上定义的分析概念。全球分析是 对物体的整体几何和拓扑性质的研究 一个空间，通过拼凑当地的信息。的应用 这些数学领域的其他科学包括 复杂的分子结构，液-气边界， 宇宙的大尺度结构

The principal investigator will continue his study of minimal surfaces in spaces of constant mean curvature. In particular he will study surfaces of higher genus such as the torus embedded in the sphere. The techniques to be used involve integrable systems in infinite dimensional spaces. This technique is very different from the standard methods used to study these problems thus far. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.