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

非线性色散方程的重要应用范围从凝聚态到非线性和激光光学，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。在这段时间里，新技术和突破性的想法，主要是从谐波分析，打开了大门，以解决这些问题。 加州大学洛杉矶分校的陶教授在调和分析在Korteweg de弗里斯方程、非线性薛定谔方程和波动图等相关领域的应用方面作出了开创性的贡献。陶教授将在拉斯克鲁塞斯的新墨西哥州州立大学发表题为“非线性色散和波动方程”的系列讲座，共十场。虽然陶和其他人的技术相当新，仍然具有巨大的新应用潜力，但一些关键思想现在可以被视为“原则”。这些将在陶的讲座中阐述。一些主要的应用程序，这一阶段，以及开放的问题，也将进行讨论。讲座应该感兴趣的任何人在谐波分析，偏微分方程，或波传播的数学物理工作，退伍军人和新人一样。

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.