Mathematical Sciences: Cohomology of Operator Algebras

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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.