Partial Differential Equations

Partial Differential Equations (PDE) are ubiquitous in essentially all sciences and engineering, and have important interactions with several branches of pure mathematics, including Geometry and Probability.

Our research in PDE covers a wide variety of topics and connections to other areas, including: regularity and smoothness of solutions to nonlinear PDE; free boundary problems and minimal surfaces; nonlocal equations arising in probability, physics, or geometry; reaction-diffusion equations, including those modelling population dynamics; isoperimetric problems and other geometric inequalities; PDEs arising in fluid mechanics, statistical mechanics, and relativistic quantum mechanics.