Mathematical Sciences: Structure of Operator Algebras

这是一个数学研究项目， 算子代数，与其他几个领域的附带影响 数学。 Hilbert空间上的算子代数具有长 被用来表示数学结构的多样性， 包括理论物理学中出现的一些问题。 校长 调查人员将追查一个非常富有成效的 关于如何度量算子代数的大小的想法 相对于包含它的更大的代数。 他将调查并利用 因子的子因子，共形场论，纽结理论， 统计力学、完全可积系统和量子力学 组 特别是，将尝试给出一个 某些纽结不变量的显式三维定义 迄今为止仅通过编织物或二维投影来限定。

This is a project for mathematical research in the theory of operator algebras, with collateral impact in several other areas of mathematics. Algebras of operators on Hilbert space have long been used to represent a diversity of mathematical structures, including some that arise in theoretical physics. The principal investigator will pursue consequences of an extremely fruitful idea of his about how to measure the size of an operator algebra relative to a larger algebra that contains it. He will investigate and exploit connections between subfactors of factors, conformal field theory, knot theory, statistical mechanics, completely integrable systems, and quantum groups. In particular an attempt will be made to give an explicit three-dimensional definition of certain knot invariants hitherto only defined via braids or two-dimensional projections.