9423719 Kuhn Homotopy theory and representation theory have quite distinct origins, with the former being motivated by the desire to understand the global structure of geometric objects such as manifolds, and the latter evolving out of the study of how algebraic structures act as symmetries on vector spaces. Professor Kuhn is continuing his study of the common ground between these subjects, as typified by his development of "generic representation theory," which was originally inspired by work by topologists on the Steenrod algebra, but which seems to offer new powerful tools for understanding completely representation theoretic topics such as the modular representations of the finite general linear groups and the MacLane homology of algebraic K-theorists. Among the specific questions being studied are ones dealing with homotopy "at a large prime," topological realization questions, and the relation between stable K-theory and MacLane homology. Both homotopy theory and representation theory are mathematical subjects in which one is trying to discover, and ultimately classify, fundamental "building blocks" of structure: homotopy dealing with deformations of geometric objects such as higher dimensional surfaces, and representation theory being concerned with symmetries of discrete algebraic objects such as configurations of lines and planes. Professor Kuhn is continuing his study of some of the common ground between these, using algebraic tools developed by him that were inspired by homotopy theoretic experiences. ***
