Operator algebras and operator theory

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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.