Benson This award supports work on representations and cohomology of finite and compact Lie groups. There are three areas which will be investigated. The first is an investigation of the representation theory and cohomology of finite groups, primarily over fields of prime characteristic. The second involves understanding the cohomology of compact Lie groups, by extending current methods from the finite case. The third is aimed at constructing maps between classifying spaces of finite and compact Lie groups. The research supported concerns the representation theory of finite groups. A group is an algebraic object used to study transformations. Because of this, groups are a fundamental tool in physics, chemistry and computer science as well as mathematics. Representation theory is an important method for determining the structure of groups. ***
