Modular Representations of Finite Groups, Codes and Projective Geometry Over Finite Fields

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AbstractThe planned research lies at the junction of three areas, modular representations of finite groups, finite projective geometry and the theory of designs and their codes. Under this project, Sin will continue to develop a general framework in which techniques of representation theory and group cohomology can be applied to attack combinatorial problems about codes and geometries, at the same time studying how the latter areas may provide a more geometric viewpoint in representation theory. The successful outcome of this research should lead to further new methods and results in all three theories and speed the circulation of ideas among them.