Mathematical Sciences: K-Theory and Other Invariants of C*-Algebras

Zhang将继续研究C*-代数的各种不变量，包括实rand，拓扑稳定rand，指数rand和长度，格拉斯曼空间的C*-投影长度，以及某些C*-代数的酉群和格拉斯曼空间的同伦群。他还将继续研究乘子代数在k理论及其相关C*-代数的扭转子群方面的内部结构。这个项目的一般数学领域在希尔伯特空间算子的代数理论中有其基础。运算符可以被认为是有限或无限的复数矩阵。特殊类型的运算符通常放在一个代数中，自然地称为运算符代数。这些抽象对象有各种各样的应用。例如，它们在结理论中发挥着关键作用，而结理论目前正被用于研究DNA的结构，它们在非交换几何中具有重要的基础意义，而非交换几何在物理学中正变得越来越重要。

Zhang will continue his research on various invariants of C*- algebras, including the real rand, the topological stable rand, the exponential rand and length, the C*-projective length of the Grassmann space, and the homotopy groups of the unitary group and the Grassmann space of certain C*-algebras. He will also continue his investigation on the internal structure of the multiplier algebras in terms of the K-theory and its torsion subgroup of the associated C*-algebra. 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.