Mathematical Sciences: An NSF-CBMS Regional Conference on Applications of Operator Algebras to Knot Theory and Mathematical Physics; June 5-11, 1988

从一开始，沃恩·琼斯在1981年成功地获得了II1型子因子的指数理论，这被认为是算子代数理论的重大进步。然而，没有预见到的是，这一理论对数学的其他分支产生了显著的影响，特别是对纽结理论。Jones工作的算子代数设置通过对Jones和其他作者得到的Alexander多项式的推广，使纽结理论发生了革命性的变化。最近，许多数学家开始认识到琼斯的指数理论是数学物理甚至数学生物学中的一个强有力的工具。这次会议，琼斯教授做了十次系列讲座，将记录到目前为止所取得的进展，指出作为子因子指数理论的直接结果而在数学的不同分支之间发展起来的联系，并探索许多数学家和科学家正在考虑的在不同领域的迷人应用。

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.