Mathematical Sciences: Studies in Semigroups of Endomorphisms, Operator Algebras, and Numerical Quantum Mechanics

Arveson将研究几个非交换的领域 涉及冯诺依曼代数和C*-代数的量子化分析 指数理论，以及非交换领域的作用， Bratteli，Elliott，Evans和Kishimoto在数值量子中 力学 研究将涉及指数理论和 因子自同态半群的分类理论， 与这种半群相关联的C*-代数的结构，以及 离散化C ~*-代数的性质 正则对易关系 这个项目的一般数学领域有其基础 希尔伯特空间算子的代数理论。 运营商 可以被认为是复数的有限或无限矩阵 号码 特殊类型的运算符通常放在 代数，自然称为算子代数。 这些抽象 物体的应用范围之广令人惊讶。 比如说， 它们在纽结理论中起着关键作用，而纽结理论目前 被用来研究DNA的结构， 在非对易几何中的重要性， 在物理学中变得越来越重要。

Arveson will investigate several areas of non-commutative analysis involving von Neumann algebras and C*-algebras, quantized index theory, and the role of the non-commutative spheres of Bratteli, Elliott, Evans and Kishimoto in numerical quantum mechanics. The research will involve the index theory and classification theory of semigroups of endomorphisms of factors, the structure of the C*-algebras associated to such semigroups, and the properties of C*-algebras associated with the discretized canonical commutation relations. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA, and they are of fundamental importance in noncommutative geometry, which is becoming increasingly important in physics.