This award supports research on the representation theory of finite groups and group cohomology. The principal investigator will work on: (1) functors on categories constructed from bisets; (2) Alperin's conjecture for specific classes of groups; (3) development of computer software for representation theory; (4) Broue's conjecture on isotypies of blocks; (5) the structure of Brown's complex of p-groups. The two conjectures mentioned are considered fundamental in the representation theory of finite groups, and solutions of either of these would have considerable ramifications in ths area. 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, computer science, and biology as well as mathematics. Representation theory is an important method for determining the structure of groups.
