This project is concerned with various problems in ring theory. The principal investigator will investigate the Jacobian Conjecture using differential operators, a general theory of lattices and cocompact lattices in the automorphism groups of simplicial trees, and an elaboration of Asamura's theorem in algebras with polynomial fibres. In conjunction with a postdoctoral associate, the principal investigator will work on a structure theory for groups acting freely on R-trees.