Mathematical Sciences: Cohomology of Operator Algebras

吉尔费瑟教授将通过将自然拓扑结构扩展到非交换环境来研究算子代数中的上同调。期望他的工作将导致更好地理解非自伴随算子代数的上同调，因此将对我们对这些代数的理解产生实质性的影响。本研究起源于希尔伯特空间上算子的研究。希尔伯特空间算子本质上是复数的无限矩阵。这些运算符在应用科学的各个领域以及纯数学中都有应用。这种类型的研究是试图对这类物体的某些重要类别进行分类。

Professor Gilfeather will investigate cohomology in operator algebras by extending natural topological constructions to a non-commutative setting. The expectation is that his work will lead to a better understanding of the cohomology of non- selfadjoint operator algebras and will therefore have a substantial impact on our understanding of these algebras. This research originates in the study of operators on Hilbert space. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important categories of such objects.