# Graduate Student / Postdoc Seminar

#### Riemann-Hilbert Problems, Orthogonal Polynomials and Computation

**Speaker:**
Tom Trogdon

**Location:**
Warren Weaver Hall 1312

**Date:**
Friday, December 13, 2013, 1 p.m.

**Synopsis:**

The Fokas-Its-Kitaev Riemann-Hilbert problem has well-understood applications to the asymptotic analysis of both orthogonal polynomials and random matrices. This Riemann-Hilbert problem and the Deift-Zhou method of nonlinear steepest descent are the key ingredients in a proof of universality for unitary invariant random matrix ensembles. I will review the theory of Riemann-Hilbert problems and discuss their numerical solution. These ideas are used to demonstrate how the Fokas-Its-Kitaev Riemann-Hilbert problem is an important tool for the computation of Jacobi operators, Gaussian quadrature rules, interpolation formulae and statistical quantities for finite-dimensional random matrices.