This award provides support for a meeting, held at Brown University in the spring of 2008, on current topics in analysis of nonlinear wave equations, with presentations by leading researchers in the areas of harmonic analysis techniques, dispersive waves, stability analysis, kinetic theory, free boundaries and relativistic equations. The conference encourages and financially supports participation by students and members of groups underrepresented in the mathematical sciences.
Nonlinear waves occur in many fundamental many physical problems and have a central place in modern theory of nonlinear partial differential equations. Historically the foci of research for nonlinear wave equations have been in classical field theories, such as in the study of nonlinear Klein-Gordon equations, the Maxwell- Dirac system, and the Yang-Mills system. More recently there have been explosive and exciting developments in many new directions for nonlinear wave equations, including for dispersive equations such as KdV and nonlinear Schrödinger equations, for kinetic equations including Boltzmann and Vlasov models, in fluid dynamics including the incompressible Euler equations, for free boundary problems, for the Einstein field equations in general relativity, and for geometric wave equations such as wave maps and Schrödinger maps. This conference brings together leading experts in a great variety of different areas of research in nonlinear wave equations, to stimulate interactions between their different points of view that should be of mutual benefit to all the participants. In particular, the conference will be especially beneficial to young researchers, including graduate students and postdocs.
