Mathematical Sciences: Research on Spectral Geometry and onHilbert's Fourth Problem

首席研究员将继续他在黎曼流形上的光谱几何研究。特别地，他将考虑黎曼流形族，其联合谱决定度规。Szabo教授还将继续研究德萨古空间及其与希尔伯特第四问题的关系。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 continue his research in spectral geometry on Riemannian manifolds. In particular he will consider families of Riemannian manifolds whose joint spectrum determines the metric. Professor Szabo will also continue his investigation of the Desarguesian spaces and their relationship with Hilbert's fourth problem. 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.