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.
