**Complex Analysis and PDE Group at Brown University **

Analysis at Brown encompasses partial differential equations, complex function theory, harmonic analysis, and operator theory. The connections among all of these areas are a specialty of ours. 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.

### Participating Faculty

**Xuwen Chen**, Tamarkin Assistant Professor of Mathematics.

**Brian Cole**, Professor
of Mathematics.

**Constantine Dafermos**, Alumni-Alumnae University Professor of Applied Mathematics.

**Francesco Di Plinio**, Tamarkin Assistant Professor of Mathematics.

**Yan Guo**, Professor of Applied Mathematics.

**Justin Holmer**, Associate Professor of Mathematics.

**John Mallet-Paret**, Professor of Applied Mathematics.

**Govind Menon**, Assistant Professor of Applied Mathematics.

**Jill Pipher**, Professor
of Mathematics.

**Walter Strauss**, Professor
of Mathematics and Applied Mathematics.

**Sergei Treil**, Professor
of Mathematics.

**John Wermer**, Professor
Emeritus of Mathematics.