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

Zhang将继续研究C* 的各种不变量- 代数，包括真实的兰德，拓扑稳定兰德， 指数兰德和长度，C*-投影长度的 Grassmann空间，酉群的同伦群， 一类C ~*-代数Grassmann空间 他还将继续 他对乘法器内部结构的研究 代数的K-理论及其挠子群 伴随C*-代数 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。

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.