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29/06/2011, 16:30 — 17:30 — Amphitheatre Pa1, Mathematics Building

Ron Douglas, *Texas A&M University*

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Operator Theory and Complex Geometry

One approach to the study of multivariate operator theory on Hilbert space is the study of algebras of operators. Many algebras of operators act on natural Hilbert spaces of holomorphic functions defined on some complex domain in ${\u2102}^{m}$. Examples are the algebras of bounded multipliers on the Hardy and Bergman spaces for the unit ball and polydisk in ${\u2102}^{m}$. One approach to the study of such algebras is to adapt the complex geometric methods of M. Cowen and the author to the context of Hilbert modules over the polynomial algebra in several variables. In this talk, I will describe this line of study with an emphasis on concrete examples as well as a focus on several results in operator theory whose proof rests on concepts and techniques from algebraic and complex geometry.