Riemann-Hilbert Problems - Theory and Applications

Explore the comprehensive theory and applications of Riemann-Hilbert problems through this extensive lecture series delivered at the 27th Annual PCMI Summer Session on Random Matrices. Master the fundamental theory of Riemann-Hilbert problems before delving into their sophisticated applications in inverse scattering theory. Learn to apply the nonlinear steepest-descent method to compute long-time behavior of integrable systems and tackle complex problems in random matrix theory and orthogonal polynomials. Progress through eight structured parts that systematically build from basic theoretical foundations to advanced computational techniques. Access accompanying lecture notes to reinforce your understanding of these powerful mathematical tools used in modern analysis and mathematical physics. Benefit from instruction designed for mathematics educators, researchers, and advanced students seeking intensive mathematical training in this specialized field.