NSF/CBMS Regional Conference in the Mathematical Sciences: Nonlinear Dispersive and Wave Equations

非线性色散方程非常重要的应用范围从凝聚态到非线性光学和激光光学，它们的数学研究可以追溯到100多年前。即便如此，许多基本的数学问题——包括适定性——直到最近几年才得到严格的解决。在此期间，主要来自谐波分析的新技术和突破性思想为解决这些问题打开了大门。美国加州大学洛杉矶分校的Terence Tao教授在将谐波分析应用于Korteweg de Vries方程、非线性薛定谔方程和波动图等相关领域方面做出了开创性的贡献。陶教授将在拉斯克鲁塞斯的新墨西哥州立大学进行10场题为“非线性色散和波动方程”的系列讲座。由于陶和其他人的技术是相当新的，并且仍然具有巨大的新应用潜力，许多关键思想现在可以被视为“原则”。这些将在陶的讲座中展开。我们还将讨论这一阶段的一些主要应用，以及尚未解决的问题。任何从事谐波分析、偏微分方程或波传播数学物理研究的人，无论是老手还是新手，都应该对这些讲座感兴趣。

Immensely important applications of nonlinear dispersive equations range from condensed matter to non-linear and laser optics, and their mathematical study dates to well over 100 years. Even so, many fundamental mathematical questions - including well-posedness - have been rigorously addressed only in the last few years. During this time, new techniques and break-through ideas, largely from harmonic analysis, have opened the door to the resolution of such problems. Professor Terence Tao of the University of California, Los Angeles has made ground-breaking contributions in the applications of harmonic analysis to the related areas of the Korteweg de Vries equation, nonlinear Schroedinger equations, and wave maps.Professor Tao will deliver a series of 10 lectures entitled "Nonlinear Dispersive and Wave Equations" at New Mexico State University in Las Cruces. While the techniques due to Tao and others are fairly new and still hold tremendous potential for new applications, a number of the key ideas can now be deemed `principles'. These will be laid out in Tao's lectures. Some of the main applications to this stage, as well as open problems, will also be discussed. The lectures should be of interest to anyone working in harmonic analysis, partial differential equations, or the mathematical physics of wave propagation, veterans and newcomers alike.