Mathematical Sciences: Deformation Problems from Geometry and Algebra

点击翻译按钮获取中文摘要

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.