Asymptotic analysis of Riemann-Hilbert problems, d-bar problems, and a few applications

First I'll define all the terms in the title. Then I'll discuss two applications: integrable nonlinear partial differential equations, and orthogonal polynomials. Then there will be a discussion regarding asymptotic analysis of hybrid Riemann-Hilbert-d-bar problems. If all goes well there'll be time remaining to see the machinery in action on one of the applications: either the asymptotic behavior of a nonlinear pde, or the asymptotic behavior of orthogonal polynomials. The point to using d-bar methods is to handle reduced regularity assumptions and still obtain global asymptotics with precise control on the error terms.