Conference on Geometric Methods in Infinite-dimensional Dynamical Systems

Brown University, Providence RI

Investigators

Abstract

Geometric methods play a central role in dynamical systems and its applications. To showcase recent theoretical breakthroughs and to outline challenges and opportunities for applications, in particular in areas in which dynamical systems have not been utilized much, a conference on geometric methods in infinite-dimensional dynamical systems will be held November 4-6, 2011, at Brown University. The conference will be centered around four mathematical themes: data assimilation, geometric singular perturbation theory, nonlinear optics, and traveling waves. There will be around 15 long and 10 short talks. Several of the longer talks and at least half of the short talks will be given by younger participants. A poster session will give other younger participants the opportunity to present their results, and a future-directions panel discussion will feature a broad-scale discussion of the challenging theoretical questions and applied problems involving infinite-dimensional dynamical systems. Geometric methods are essential for the development of mathematical tools and for applications in areas such as oceanography, data assimilation, neuroscience, nonlinear optics, and pattern formation. At present, new geometric methods are being developed to expand our knowledge of multi-dimensional waves, pulses propagating in structured media, the dynamics of defects and other localized patterns, and in the dynamics on neuron populations. Another emerging challenge to dynamical systems theory is to develop mathematical techniques for data assimilation, which is used in weather forecasts and climate research. By advertising these opportunities to younger and senior participants alike, this conference could stimulate additional research in this field and its applications.