Research interests: Partial differential equations and harmonic analysis
Luke holds an MMath from the University of Warwick, where he focused on analysis modules. As part of his first degree, he worked on a project on the solvability of Stokes equation, a low speed approximation to the Navier-Stokes equations. Currently Luke is investigating the solvability/existence of solutions to linear elliptic and parabolic PDEs with rough coefficients on Lipschitz domains. When he isn't working, Luke enjoys the outdoors and is excited by the opportunities for walking, cycling and climbing afforded by living in Edinburgh.