McLaughlin's research is in approximation theory, random matrix theory, integrable nonlinear pdes, and applications.

## ∂- problems and Riemann-Hilbert problems

The semi-classically scaled ∂- problem associated to the Davey-Stewartson equation - uncharted territory.

normal matrix model eigenvalue density with quartic potential

## Approximation Theory

Zeros of degree 200 Taylor polynomial for cosh(z). The Dashed and solid lines represent the "Szego curve" for this case.

Zeros of Taylor polynomials of Riemann's Xi function, with degree up to 200

Here are notes from the lecture I gave on April 6, in the Inverse Problems seminar.

###### Dispersive ringing in PDEs

###### 2D histogram in Normal Random Matrices

###### Tiling of a hexagonal domain by rhombi