Mathematical Sciences: Integral Geometry and Related Topicsin Geometric Analysis

首席研究员将继续研究积分几何和几何分析相关领域的问题。他将尝试扩展他早期关于紧型对称空间上的极大平面变换的工作，以构造这些空间的所有对称覆盖。他还将研究最大弯曲球的特殊类的积分，并寻找更高同伦群信息。该奖项将支持积分几何一般领域的研究。一个集合的几何结构通常可以通过将集合分解成片来分析和描述。切片的几何形状通常相当简单，易于描述。分析中的主要困难通常是从切片的几何形状中重建整个集合的底层几何特征。这一数学领域的一个广为人知的应用是CAT扫描。

The principal investigator will continue his investigation of problems in integral geometry and related areas of geometric analysis. He will attempt to extend his earlier work on the maximal flat transform on a symmetric space of compact type to construct all symmetric coverings of such spaces. He will also study integrals attached to the distinguished class of maximally curved spheres and look for higher homotopy group information. This award will support research in the general area of integral geometry. The geometry of a set may often be analyzed and described by a decomposition of the set into slices. The geometry of the slices is often fairly simple and easy to describe. The main difficulty in the analysis is usually the reconstruction of the underlying geometric features of the entire set from the geometry of the slices. One well know application of this area of mathematics is the CAT scan.