Professor Phillips will investigate the concept of exponential rank in C*-algebras. In particular he will (a) obtain a better understanding of the exponential rank of algebras of matrix valued functions, and the possible connections with real rank, (b) determine the exponential rank of stable C*-algebras, and (c) further investigate the relation between real rank zero and the property weak (FU). In addition Professor Phillips will investigate the homotopy theory of inverse limits of C*-algebras. The notion of a C* algebra is an abstraction of the idea of a family of linear transformations on a space. These transformations can also be thought of as having values in the states of the space, and the property of this family which is responsible for the symbol * is that the algebra is generated by transformations whose values in these states are real numbers. The fact that these objects appear naturally in many branches of mathematics and physics make them important to study.
