Potential Theory on and Compactifications of Lie Groups and Euclidean Buildings

9704434 Ji本项目属于一般谐波分析领域。具体来说，研究者将确定对称空间的Martin紧化，并研究其拓扑性质以及包括Satake紧化在内的其他紧化类型的拓扑性质。所要使用的工具包括热核在无穷远处的渐近性。对称空间起源于连续的对称群，即李群。这些空间特别吸引人，因为它们配备了许多自然的自对称性。此外，它们还为数学的各个分支（包括代数、分析和几何）之间的相互作用提供了肥沃的土壤。

9704434 Ji This project lies in the general area of harmonic analysis. Specifically, the investigator is to determine the Martin compactification of symmetric spaces and study their topological properties along with those of other types of compactifications including the Satake compactification. The tools to be used include asymptotics at infinity of the heat kernel. Symmetric spaces arise from continuous symmetry groups known as Lie groups. These spaces are particularly appealing in that they come equipped with many natural self-symmetries. In addition, they provide a fertile ground for interaction amongst various branches of mathematics including algebra, analysis and geometry.