This proposal is concerned with the number of characters in a block of a finite group. The principal investigator will complete the reduction of his conjecture on this to the case of almost simple groups. He will also verify it for as many such groups as possible and will search for a simpler direct proof of it. 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.
