Riemann-Hilbert Problem and Integrable Systems

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AbstractZhouThis proposal project covers, perturbation theory for focusing NLS,multiple orthogonal polynomials, oscillatory Riemann-Hilbertproblems with nonanalytic phase, zero dispersion of focusing NLS,orthogonal rational functions, and Janossy densities in the randommatrix theory. All these problems require Riemann-Hilbert problemtechniques to study.This project is an effort to develop further the analytic aspectsand the interdisciplinary applications of the fruitful field of theRiemann--Hilbert problem method, with the balance between itsintellectual and educational merits. The study of Riemann--Hilbertproblem has applications in several areas of mathematics andmathematical physics, including partial differential equations,statistical mechanics and combinatorics.