Potential Theory on and Compactifications of Lie Groups and Euclidean Buildings

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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.