Ken McLaughlin

Zeros of Taylor polynomials
and Number Theory

A Riemann-Von Mangoldt formula for zeros of Taylor approximants of Riemann's Xi function (work with Bob Jenkins).
Asymptotic behavior of the Partition Function
Rigorous analysis in the two-cut regime.

Work with Tom Claeys and Tamara Grava
The Soliton Resolution Problem
Rigorous derviation of the long-time asymptotic behavior of the NLS equation for general initial conditions.

Work with Michael Borghese and Bob Jenkins
Spectral Approach to D-bar problems.
First spectrally convergent numerical method for D-bar problems.

Work with Christian Klein

Chair, Department of Mathematics at Colorado State University

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

For Graduate Students: two possible courses of study

For research in nonlinear PDEs

Analysis (517)

Complex variables (519)

Linear Algebra (560)

Partial Differential Equations (545 and 546)

Functional Analysis (from 618)

Advanced PDEs (645 and 646)

For research in random matrix theory and combinatorics

Analysis (517)

Complex variables (519)

Combinatorics (501 and 502)

Linear Algebra (560)

Probability Theory (STAT 620)

Advanced Complex Variables (619)

Join our Research Group!

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

Fort Collins Weather

Find more about Weather in Fort Collins, CO

Click for weather forecast

Glacier Basin webcam at Rocky Mountain National Park

Fall Colors in Fort Collins

Photo courtesy of M. Theresa T-R McLaughlin

Some of the material on this page is based on work supported in part by the National Science Foundation under grant numbers DMS-0200749, DMS-0451495, DMS-0800979, and DMS-1401268 (McLaughlin). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Zeros of Taylor polynomials and Number Theory

Asymptotic behavior of the Partition Function Rigorous analysis in the two-cut regime.

The Soliton Resolution Problem Rigorous derviation of the long-time asymptotic behavior of the NLS equation for general initial conditions.

Spectral Approach to D-bar problems. First spectrally convergent numerical method for D-bar problems.

Chair, Department of Mathematics at Colorado State University

∂- problems and Riemann-Hilbert problems

Approximation Theory

For Graduate Students: two possible courses of study

For research in nonlinear PDEs

For research in random matrix theory and combinatorics

Join our Research Group!

Dispersive ringing in PDEs

2D histogram in Normal Random Matrices

Tiling of a hexagonal domain by rhombi

Fort Collins Weather

Glacier Basin webcam at Rocky Mountain National Park

Fall Colors in Fort Collins

Photo courtesy of M. Theresa T-R McLaughlin

Zeros of Taylor polynomials
and Number Theory

Asymptotic behavior of the Partition Function
Rigorous analysis in the two-cut regime.

The Soliton Resolution Problem
Rigorous derviation of the long-time asymptotic behavior of the NLS equation for general initial conditions.

Spectral Approach to D-bar problems.
First spectrally convergent numerical method for D-bar problems.