Mathematical Sciences: The Geometry of Cycle Spaces and Moduli Spaces

主要研究人员将继续研究微分几何和代数几何中的问题。特别是，他们将通过特征类的方法来研究Chow品种的结构。结果可能与博特周期性、霍奇猜想和舒伯特演算有关。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 investigators will continue their investigation of problems in differential and algebraic geometry. In particular they will investigate the structure of Chow varieties via the method of characteristic classes. Results are expected to have relationships with Bott periodicity, the Hodge conjecture, and the Schubert calculus. 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.