Mathematical Sciences: Structure of Operator Algebras

琼斯教授将研究子因子的例子（从有限维度和无限维度的方法）。他的技术将涉及使用环群表示、结理论和统计力学。特别重要的是试图理解统计力学和结理论之间的对应关系。这将通过观察大的结和一个称为Baxterization的过程来解决。琼斯的工作以希尔伯特空间算子的代数理论为基础。这些是在无限维空间中的线性函数族。他感兴趣的是这些代数的巢是如何相互融合的。这个看似技术性的课题对数学和物理的许多其他领域都有非常重要的影响，包括结理论和三维流形理论（拓扑）和统计力学（物理）。

Professor Jones will study examples of subfactors (both from finite dimensional and infinite dimensional methods). His techniques will involve the use of loop group representations, knot theory, and statistical mechanics. Of special importance is an attempt to understand the correspondence between statistical mechanics and knot theory. This will be approached both by looking at large knots and a procedure called Baxterization. Jones' work has its basis in the theory of algebras of Hilbert space operators. These are families of linear functions on a certain type of infinite dimensional space. He is interested in how nests of these algebras fit inside one another. This seemingly technical subject turns out to have very important implications for a large variety of other areas of mathematics and physics including knot theory and the theory of three dimensional manifolds (topology) and statistical mechanics (physics).