Mathematical Sciences: Modular Representation of Finite Groups

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This project is an investigation into the representation theory of finite groups over fields of prime characteristic. Of particular interest is the structure of modules. Abstract structures such as cohomology rings and varieties of modules will be used to study specific properties of modules. Progress here will help to explain the curious phenomena in the cohomology of irreducible modules and will have an impact on the module theory of finite group algebras. The research supported concerns the representation of finite groups over fields. The structure of the groups is realized through the action of the groups as transformations on spaces. This is currently one of the most active areas of pure algebra.