Mathematical Sciences: Matrix Functions on Riemann Surfaces

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Professor Clancey will study the matrix function theory of closed Riemann surfaces. Specifically, he will investigate problems in interpolation of zero-pole data and interpolation of values with bounds (Nevanlinna-Pick interpolation). These problems are important in real world questions and the research will attempt to provide explicit solutions. Professor Clancey's research is on the interface between the theory of complex valued differentiable functions and the theory of Hilbert space operators. 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 families of such objects.