Operator algebras and operator theory

算子理论和算子代数理论兴起于20世纪，部分原因是需要为新兴的量子物理学领域提供数学工具。虽然这个数学分支和物理学之间仍然有重要的联系，但物理学的量子化已经延续到数学中，在数学中，某些数学结构只有通过考虑它们作为“非交换”实体的特征才能揭示（或分类）。这种观点在现代分析和代数中尤其普遍，特别是在算子代数理论中。我的研究计划的目标是通过对序，凸性和拓扑的研究来推进算子代数理论，并将算子代数方法应用于单算子理论中的问题。

Operator theory and the theory of operator algebras arose in the twentieth century, in part, out of a need to provide the mathematical tools for the newly emerging field of quantum physics. While there remain important connections between this branch of mathematics and physics, the quantisation of physics has carried over to mathematics, where certain mathematical structures are revealed (or classified) only by taking into account their features as "noncommutative" entities. This view is especially prevalent in modern analysis and algebra, and in operator algebra theory in particular. The goal of my research program is to advance operator algebra theory through the study of order, convexity, and topology, and to apply operator-algebraic methods to problems in single operator theory.