Introduction to asymptotic analysis of Riemann - Hilbert problems and applications

Ken McLaughlin


Abstract:

Lecture 1. (Wednesday, June 29) A few guiding principles for the asymptotic analysis of some Riemann-Hilbert problems.

Lecture 2. (Thursday, June 30) Equilibrium measures and level sets of quadratic differentials, applications to asymptotics of orthogonal polynomials.

Lecture 3 (Friday,`July 1). Singular limits of integrable systems: Toda lattice and nonlinear Schrödinger equations.

Lecture 4, (Tuesday, July 5) Discrete orthogonal polynomial ensembles and random tiling problems.

Lecture 5. (Thursday, July 7) TBA.