Special meeting: Dynamical systems and evolution equations, CRM

特别会议：动力系统和演化方程，CRM

• 批准号: 0803140
• 负责人: Clarence Wayne
• 金额: --
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-04-15 至 2009-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0803140&HistoricalAwards=false
• 关键词: Special; meeting; Dynamical; systems; evolution

The focus of the thematic program semester of winter 2008 at the CRM is on dynamical systems, interpreted in a broad sense so as to include applications to fundamental problems in differential geometry as well as in mathematical physics. Topics that are considered include:(1) the interplay between dynamical systems and PDE, in particular in the context of Hamiltonian systems,(2) geometric evolution equations such as Ricci flows and extrinsic curvature flows, (3) spectral theory and its relationship to Hamiltonian dynamics, and(4) Floer theory and Hamiltonian flows. In the past several years there have been dramatic achievements in these four areas, representing progress on a number of the most basic and difficult questions in this field. These advances have had a broad impact on recent progress in geometry and topology, and they also shed light on basic physical processes, such as nonlinear wave phenomena, that are modeled by ordinary and partial differential equations.The purpose of this program semester is to bring together members of the diverse international community of researchers who have an interest in these topics, to give a series of advanced-level courses on relevant subject matter so as to make the topic accessible to new researchers in the field, and to bring into discuss the perspectives and general indications for the next advances and directions of progress in the area.The central focus of the theme semester of winter 2008 at CRM is dynamical systems. The theory of dynamical systems is concerned with the description of the evolution of systems depending on time. Such systems are fundamental, and appear very commonly in the modeling of physical, chemical and biological phenomena, as well as in geometry and many other areas of mathematics. In the past several years there have been dramatic achievements in the area of dynamical systems, including the proof of Poincaré conjecture by G. Perelman (an event known to the public through the drama of the Fields medal awards in 2006). These advances have had a broad impact on recent progress in geometry and topology. The modern theory of dynamical systems has also been fundamental in the study of many basic physical processes, and their modeling by ordinary and partial differential equations. The purpose of this program semester is to bring together representatives of the diverse international community of researchers who have an interest in these topics. Its activities will comprise (1) a series of advanced-level courses on the subject matter, so as to make the field available to students and new researchers, (2) to host discussions of the perspectives and future directions for the next advances and areas of progress in the field.

2008年冬季在CRM上的主题计划学期的重点是动态系统，从广义上讲，以包括在差异几何以及数学物理学中的基本问题中应用。所考虑的主题包括：（1）动态系统与PDE之间的相互作用，特别是在汉密尔顿系统的背景下，（2）几何进化方程，例如Ricci流和外部曲率流，（3）光谱理论及其与汉密尔顿动力学的关系及其与汉密尔顿动力学的关系，以及（4）浮动理论和汉密尔顿式的流动。在过去的几年中，这四个领域取得了巨大的成就，代表了该领域许多最基本和最困难的问题的进步。这些进步对几何和拓扑的最新进展产生了广泛的影响，它们还阐明了基本的物理过程，例如非线性波浪现象，这些过程是由普通和部分差分方程式建模的，该课程学期的目的是召集潜水者国际研究员的兴趣，这些研究人员对这些主题的访问和领域的访问相关，以使一系列领域的领域相关，以使其成为一系列相关的研究，以使其相关，以使其相关，以使其成为一系列领域，以使其成为一系列领域，以使其成为一系列的领域，因此，与他们相关的研究者，以此为方面的研究，为了讨论该地区下一个进步的观点和一般迹象。动态系统的理论涉及对系统演变的描述。这样的系统是基本的，并且通常在物理，化学和生物学现象以及几何和许多其他数学领域的建模中出现。在过去的几年中，动态系统领域取得了巨大的成就，包括G. Perelman的庞加莱猜想证明（G. Perelman）（通过2006年的《田间奖章奖》颁发的公众闻名）。这些进步对几何和拓扑的最新进展产生了广泛的影响。动态系统的现代理论在研究许多基本物理过程及其通过普通和部分微分方程的建模方面也是基础。该计划学期的目的是将代表对这些主题感兴趣的国际研究人员的不同国际社会汇集在一起​​。它的活动将完成（1）一系列有关该主题的高级课程，以便使学生和新研究人员可以使用该领域，（2）主持有关该领域进步和进步领域的观点和未来方向的讨论。