I am currently a third-year Dickson Instructor in the Department of Mathematics at the University of Chicago. I will be on the job market during the 2026–2027 academic year.
I am interested in the qualitative and quantitative behavior of solutions to partial differential equations, especially models arising in fluid mechanics and kinetic theory. My research focuses on energy methods, regularity theory, and stability mechanisms for nonlinear and nonlocal equations.
Please feel free to contact me with any questions about my work at wgolding@uchicago.edu.
Some ongoing and upcoming events:
My research is in partial differential equations and kinetic theory, with particular interest in regularity, stability, and the qualitative and quantitative behavior of solutions to equations arising in fluid mechanics and statistical physics.
Below is a list of publications and preprints, with links to available arXiv and journal versions.
Below is a list of recent courses I have taught at the University of Chicago.
This is the second in a sequence of mathematics courses for physical sciences majors. It covers multivariable calculus: functions of more than one variable, parameterized curves and vector fields, partial derivatives and vector derivatives (div/grad/curl), double and triple integrals, line and surface integrals, and the fundamental theorems of vector calculus in two and three dimensions (Green/Gauss/Stokes).
This is the third in a sequence of mathematics courses for physical sciences majors. It covers differential equations: first and second order ODE, systems of ODE, damped oscillators and resonance, Fourier series and Fourier transforms, Laplace transforms, and solutions of the heat and wave equations.
This is the first in a sequence of mathematics courses for physical sciences majors. The first part of the course covers infinite sums: convergence of infinite sequences and series, Maclaurin and Taylor series, complex numbers and Euler's formula. The second part covers elementary linear algebra: linear equations, vectors and matrices, dot products, cross products and determinants, applications to 3D geometry, eigenvectors and diagonalization.
This course covers the mathematical foundations of quantum mechanics, including abstract linear algebra (vector spaces, bases, linear operators, inner products and orthogonality) and partial differential equations (with an emphasis on techniques relevant to solving Schrödinger's equation: series solutions of second order ODE, orthogonal functions, eigenfunctions and Sturm-Liouville theory, separation of variables).