Conference on Nonlinear Waves

该奖项为2008年春季在布朗大学举行的关于非线性波动方程分析的当前主题的会议提供支持，并由谐波分析技术，色散波，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进行演讲。 会议鼓励并资助学生和数学科学中代表性不足的团体成员的参与。非线性波出现在许多基本的物理问题中，在非线性偏微分方程的现代理论中占有中心地位。 历史上，非线性波动方程的研究焦点一直在经典场论中，如非线性Klein-Gordon方程，麦克斯韦-狄拉克系统和杨-米尔斯系统的研究。 最近，非线性波动方程在许多新的方向上取得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，以及几何波动方程，如波映射和薛定谔映射。本次会议汇集了非线性波动方程各个不同研究领域的顶尖专家，以激发他们不同观点之间的互动，这对所有参与者来说都是互惠互利的。特别是，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.