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Stability and hyperbolicity of polynomials and entire functions (SHPEF)
Start date: Aug 1, 2010, End date: Jul 31, 2015 PROJECT  FINISHED 

The project is devoted to the theory, algorithms and applications of hyperbolic and stable multivariate polynomials. This line of research is meant to lead to new fundamental results in analysis, matrix and operator theory, combinatorics, and theoreticalcomputer science.The central goal of the project is to develop a comprehensive, seamless, theory of hyperbolic and stable multivariate polynomials. The four areas and four objectives of the project are as follows:Classical analysis: revisit and expand the theory of hyperbolic and stable polynomials and entire functions in both the univariate and the multivariate setting. Applications: apply the theory of hyperbolic and stable polynomials to problems of matrix theory,combinatorics and theoretical computer science.Operator theory: develop the theory of hypo- and hyperoscillating operators and apply it to problems of fluid dynamics. Algorithms: develop fast and accurate algorithms for testing hyperbolicity/stability and for related problems.

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