Riemann-Hilbert problem and integrable systems

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PI: Xin Zhou, Duke UniversityDMS-0300844AbstractThis project is to study various applications of the Riemann-Hilbert problem method. These applications include the perturbation theory of nonlinear Schroedinger equations and severalnewly developed areas in connection with the theory of random matrices. A book project on Riemann-Hilbert problems is also included.Riemann-Hilbert problems have been found in several important areas in mathematics in recent years. Some afore mentioned applications also have interdisciplinary impact. For example, themain application of the theory of random matrices is in physics and the study of certain perturbed differential equations enhances the understanding of signal transmissions in fibre optics.