Mathematical Sciences: Deformation Problems from Geometry and Algebra

主要研究人员将通过发展Deligne原理来继续他对几何和代数中的变形问题的研究。这些方法包括微分几何和有理同伦理论中的技巧。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 investigator will continue his investigation of deformation problems in geometry and algebra by developing a principle of Deligne. The methods include techniques from differential geometry and rational homotopy theory. 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.