Spectral Theory

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Professor Simon will study various problems in the spectral theory of orthogonal polynomials. He intends to study the zero structure of the polynomials associated to self-similar measures like the Cantor measure, thereby linking to recent research in dynamical systems and harmonic analysis. He also intends to look beyond the classical spectral theory regimes of the real line and unit circle. This research piggybacks on recent progress by Professor Simon and coworkers, extending it in new directions.Orthogonal polynomials have impacts on a wide swath of science and engineering, including filter theory in electrical engineering, problems in statistics, and recently, problems in quantum computing. The kinds of basic research that Professor Simon does, has long term spinoff in these more applied areas. Professor Simon has directly supervised over thirty graduate students and mentored about that number of postdocs. His papers and books have had considerable impact, as seen by the 8,645 citations in MathSciNet (over roughly the past ten years). He is one of a handful of mathematicians with over 5,000 citations.