This project supports a three week mathematical research institute to be organized by the American Mathematical Society during the summer of 1988. The institute will be the thirty-sixth in a series planned with the purpose of bringing together a large group of mathematicians who are interested in a particular field of mathematical research. Emphasis is placed primarily on instruction at a very high level with seminars and lectures by distinguished mathematicians in related fields. The 1988 institute will focus on "Operator Theory/Operator Algebras and Applications". During the last twenty years operator theory has come of age. The subject has developed in several directions, using new and powerful methods that led to the solutions of basic problems thought to be inaccessible in the sixties. These developments have made mutually enriching contact with other areas of mathematics, including algebraic topology and index theory, complex analysis in one and several variables, and probability theory. This institute will summarize the current progress and examine the common and unifying theories that exist in the subject.
