Mathematical Sciences: Differential Structures

主要研究人员将继续他们在微分几何、厄米几何和微分拓扑学方面的工作。特别是，他们将研究Grassmann流形中的体积最小化循环、大球面的球体纤化、分层空间、爱因斯坦度量和辛几何。这一奖项将继续支持该国最强大的微分几何项目之一。除了他们的研究之外，主要调查人员将继续为研究生和本科生的教育以及他们与高中教师和学生的工作做出强有力的贡献。该奖项将支持在微分几何和全球分析的一般领域的研究。微分几何是研究空间几何和定义在该空间上的解析概念之间的关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑性质的学科。这些领域的数学在其他科学中的应用包括复杂分子结构、液体-气体边界和宇宙的大尺度结构。

The principal investigators will continue their work in differential geometry, hermitian geometry, and differential topology. In particular, they will study volume-minimizing cycles in Grassmann manifolds, fibrations of spheres by great spheres, stratified spaces, Einstein metrics and symplectic geometry. This award will continue support for one of the strongest programs in differential geometry in the country. In addition to their research, the principal investigators will be expected to continue making a strong contribution to education at the graduate and undergraduate level as well as their work with high school teachers and students. 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.