Seminar
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Location: Bakerboard Room Abstract: In this talk I will present some results on complex orthogonal polynomials that arise in the application of Gaussian quadrature to certain integrals obtained by the classical method of steepest descent. The zeros of these complex orthogonal polynomials are optimal nodes for the computation of oscillatory integrals with high order stationary points defined on the real axis. In the case of a cubic-type potential, it is possible to analyze the asymptotic behavior of these orthogonal polynomials and their zeros by using Riemann-Hilbert techniques. Similar ideas can be used to study the partition function and the free energy of the corresponding cubic random matrix model. (Joint and ongoing work with P. Bleher, D. Huybrechs, A. B. J. Kuijlaars)
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