9401266 This research is concerned with nxn matrices over a field. The main focus is on the polynomial identities and invariants of nxn matrices. There are longstanding open problems about the ring of generic matrices and its center, as well as combinatorial problems about matrices and their identities. A secondary focus is on the nxn matrix representations of certain infinite groups, particularly the braid groups. The research supported concerns matrix theory, ring theory and the calculation of invariants. In particular, this involves an old problem of determining what mathematical functions are preserved under various transformations. This is of interest in many areas of science as well as in mathematics. ***
