Mathematical Sciences: Actions of Semisimple Groups and Discrete Subgroups

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The principal investigator will study actions of non-compact semistable Lie groups and their discrete subgroups on manifolds. He will concentrate on the geometry and topology of these actions, and will develop techniques which will complement the measure theoretic and dynamical approaches in existence. 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.