We have particular research interests in singular integral and pseudodifferential operators, wavelets and Fourier analysis, geometric measure-theoretic properties of sets, and applications of operator theory to control theory. In complex variables we have special research interests in the approximation by polynomial and rational functions and in Banach algebras. A weekly analysis seminar is held, with the active participation of graduate students, faculty, and visiting analysts.

Much of the research of the PDE group is focused on the behavior of nonlinear waves, such as the existence of periodic waves, scattering and stability theory, and the propagation of shocks and other singularities. In particular, waves that occur in shallow water theory, physical plasmas, and elastic solids are under intense study. The techniques are primarily analytical, involving a priori PDE estimates, together with methods from dynamical systems, scientific computation, and topology. Another focus of research is the fine properties of solutions of elliptic boundary problems, especially when the boundary has corners. These techniques combine harmonic analysis with elliptic a priori estimates. There is an active weekly seminar in PDE, jointly run with Applied Mathematics.