This research is concerned with the structure of classical groups over rings, as well as the structure of algebraic groups over rings and the structure of gauge groups. Topics to be studied include normal and subnormal subgroups, isomorphisms and automorphisms, and various factorization problems, including word length problems. The principal investigator will also pursue the Waring problem and other problems of additive number theory for various rings including polynomial and matrix rings. In addition, he will study systems of linear partial differential equations from the algebraic point of view. This research is in the general area of algebraic K-theory. It is concerned with a wide variety of qualitative and quantitative problems related to subgroups of algebraic groups.
