Mathematical Sciences: Groups and Geometries

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This project is concerned with utilizing geometry in the study of finite groups. The principal investigator will concentrate on Buildings and their groups, particularly Buildings associated to p-adic groups and groups of Kac-Moody type. In addition, work will be done on embedding geometries in projective space. The reseach supported is in a crucial area where several parts of mathematics intersect. This project endeavors to classify certain finite groups by using finite geometry and combinatorics. The geometric connection to the theory of reductive algebraic groups and Kac-Moody groups is important for the study of finite simple groups.