Conference on Geometric Methods in Infinite-dimensional Dynamical Systems

几何方法在动力系统及其应用中起着核心作用。为了展示最新的理论突破，并概述应用的挑战和机遇，特别是在动力系统还没有得到充分利用的领域，将于2011年11月4日至6日在布朗大学举行的无限维动力系统几何方法会议。会议将围绕四个数学主题：数据同化，几何奇异摄动理论，非线性光学和行波。将有大约15个长和10个短的会谈。一些较长的演讲和至少一半的简短演讲将由年轻的参与者主持。海报会议将给其他年轻的参与者展示他们的成果的机会，未来方向小组讨论将以具有挑战性的理论问题和涉及无限维动力系统的应用问题的广泛讨论为特色。几何方法对于数学工具的开发和在海洋学，数据同化，神经科学，非线性光学，和模式形成。目前，新的几何方法正在开发，以扩大我们的知识的多维波，脉冲在结构化介质中传播，缺陷和其他本地化模式的动态，并在神经元种群的动态。动力系统理论面临的另一个新挑战是发展用于天气预报和气候研究的数据同化数学技术。通过向年轻和资深与会者宣传这些机会，这次会议可以刺激在这一领域及其应用的更多研究。

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.