From the outset, Vaughn Jones' success, in 1981, of obtaining an index theory for Type II1 subfactors was recognized as a significant advance in the theory of operator algebras. What was not foreseen, however, is the remarkable impact that this theory has had on other branches of mathematics, particularly on knot theory. The operator algebraic setting for Jones' work has revolutionized knot theory through the generalizations of the Alexander polynomial Jones and other authors have obtained. More recently, numerous mathematicians have begun to recognize Jones' index theory as a powerful tool in mathematical physics and even in mathematical biology. This conference, with Professor Jones giving a series of ten lectures, will record the advances that have been made to date, indicate the connections that have developed among various branches of mathematics as a direct result of index theory for subfactors, and explore the fascinating applications being considered in various fields by numerous mathematicians and scientists.
