Mathematical Sciences: Toeplitz Operators, Their Spectral Properties and Related Function Algebras

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This project, which is supported by a Research in Undergraduate Institutions award, is mathematical research on algebras of analytic functions. These functions, which may be thought of as the solutions of a certain very simple system of partial differential equations, enjoy remarkable properties that have made their study fundamental to mathematics and its applications for well over a century. When they are aggregated into Banach spaces and Banach algebras of functions, they become amenable to treatment by abstract, modern methods. More specifically, Professor Gorkin will investigate algebras of bounded functions on the disk that contain all the bounded analytic functions. She will also consider Toeplitz operators with bounded symbol acting on the Bergman space of the disc (analytic functions square-integrable with respect to area measure), with emphasis on the question of when two such commute.