Mathematical Sciences: Mathematical Physics and Non- commutative Differential Geometry

主要研究循环同调和相关代数构造的应用，如代数变形理论在量子力学、微局部分析、指标理论和代数k理论中的应用。该奖项将支持微分几何和全局分析领域的研究。微分几何是研究空间几何与空间上定义的解析概念之间关系的学科。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特性。这些数学领域在其他科学中的应用包括复杂分子的结构、液气边界和宇宙的大尺度结构。

The principal investigator will study applications cyclic homology and related algebraic constructions such as the deformation theory of algebras to quantum mechanics, microlocal analysis, index theory, and algebraic K-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.