Mathematical Sciences: Projects in Modern Analysis

该奖项将支持一组研究项目， 以算子理论为中心的数学家， 算子代数 调查的一些领域将是（i） 函数希尔伯特空间上的乘法算子，（ii） 使用多变量技术的多项式亚正规性，（iii） 指数大于的不可约子因子的构造 四，（四）不变理论，Schur-Weyl对偶，张量积 单位根量子群的结构（v）膨胀理论 对于算子代数和协变系统，（vi）单参数 广义对易关系的变形，（vii）算子 由Toeplitz生成的代数与奇异积分算子 随机符号，和（八）协调技术分析 非自伴算子代数 这个研究项目的一个中心方面是调查 希尔伯特空间算子 这些物体可以被认为是 复数的无限矩阵，但它们通常以某种方式出现， 更适合各种应用。 在研究项目中， 这些调查人员通常不是单个操作员的对象， 研究的是被称为代数的大类算子。 的 这类代数的结构是研究最深入的领域之一 数学领域。

This award will support the research projects of a group of mathematicians whose work centers around operator theory and operator algebras. Some of the areas of investigation will be (i) multiplication operators on functional Hilbert spaces, (ii) polynomial hyponormality using multivariable techniques, (iii) construction of irreducible subfactors with index greater than four, (iv) invariant theory, Schur-Weyl duality, and tensor product structure of quantum groups at roots of unity, (v) dilation theory for algebras of operators and covariant systems, (vi) one-parameter deformations of generalized commutation relations, (vii) operator algebras generated by Toeplitz and singular integral operators with random symbol, and (viii) coordinatization techniques to analyze non-self-adjoint operator algebras. A central aspect of this research project is an investigation of Hilbert space operators. These objects can be thought of as infinite matrices of complex numbers but they often arise in a way more suited to various applications. In the research projects of these investigators a single operator is usually not the subject of study but rather large classes of operators called algebras. The structure of such algebras is one of the most intensively studied areas of mathematics.