Conference on Nonlinear Waves

该奖项为2008年春季在布朗大学举行的一次会议提供支持，会议主题是非线性波动方程分析的当前主题，会议由调和分析技术、频散波、稳定性分析、动力学理论、自由边界和相对论方程等领域的主要研究人员发表。会议鼓励和资助学生和在数学科学中代表性不足的小组成员的参与。非线性波出现在许多基本的许多物理问题中，并在现代非线性偏微分方程组理论中占有中心地位。一直以来，人们对非线性波动方程的研究主要集中在经典场论中，如研究非线性Klein-Gordon方程、Maxwell-Dirac系统和Yang-Mills系统。最近，非线性波动方程在许多新的方向上都有了爆炸性和令人兴奋的发展，包括色散方程如KdV和非线性薛定谔方程，动力学方程包括Boltzmann和Vlasov模型，流体动力学包括不可压缩欧拉方程，自由边界问题，广义相对论中的爱因斯坦场方程，几何波动方程如波图和薛定谔映射。这次会议汇集了各种不同领域的非线性波动方程研究领域的顶尖专家，以促进他们不同观点之间的互动，这对所有与会者都应该是互利的。尤其是，这次会议将特别有利于年轻的研究人员，包括研究生和博士后。

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.