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