Mathematical Sciences: Trace Formulas, Cyclic Cohomology, Complete Unitary Invariants and Tuples of Operators

夏教授将研究多个课题的理论， Hilbert空间算子的几乎可交换n元组 他将 关于几乎循环上同调和迹公式 交换n元组 他将研究几乎的n元组理论 无扰薛定谔算子，他将试图找到一个 的次正规元组的酉不变量的完备集 运营商 本研究涉及到Hilbert空间算子理论。 这些算子可以被认为是复数的无限矩阵 号码 它们几乎适用于纯化学的每一个分支， 应用数学 夏教授的研究目的是 分类并理解这些算子的重要族。

Professor Xia will study a number of topics in the theory of almost commuting n-tuples of Hilbert space operators. He will investigate cyclic cohomology and trace formulas for almost commuting n-tuples. He will study the theory of n-tuples of almost unperturbed Schrodinger operators and he will try to find a complete set of unitary invariants for subnormal tuples of operators. This research involves the theory of Hilbert space operators. These operators can be thought of as infinite matrices of complex numbers. They find application in almost every branch of pure and applied mathematics. The object of Professor Xia's research is to classify and understand important families of these operators.