Mathematical Sciences: Geometry of the Laplacian

主要研究人员将研究紧致流形的拉普拉斯算子和流形几何之间的关系。他将尝试确定流形的谱决定类的程度，直到有限多个拓扑类型。主要研究人员还将研究光谱与其他几何量之间的关系，如直径和注入性半径。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 study the relationship between the Laplacian of a compact manifold and the geometry of the manifold. He will attempt to determine the extent to which the spectrum of the manifold determines the class up to finitely many topological types. The principal investigator will also study the relationship between spectrum and other geometric quantities such as diameter and injectivity radius. 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.