Mathematical Sciences: Multivariable Operator Theory

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9623142 SALINAS Professor Norberto Salinas proposes to investigate systems of operators and certain types of operator algebras, such as Toeplitz C*-algebras over pseudoconvex domains with transverse symmetries, using techniques from non-commutative differential geometry and from the theory of functions of several complex variables. He also plans to use techniques from algebraic topology (more specifically from K-theory) and from non-commutative harmonic analysis. The ultimate goal of the project is a deep understanding of the joint behavior of n-tuples of operators on Hilbert space. The focus of the research will be on the spectral and c*- algebraic properties of such n-tuples. The field of multivariable operator theory has become very active in the last ten years. It is central to many mathematical applications to physics, chemistry, biology, economics, computer sciences, business, and engineering. While Professor Norberto Salinas does not plan to develop these applications, the potential for these developments are apparent from the type of technology developed in his project.