University of Maryland Spring Dynamics Conference

该奖项延续了美国国家科学基金会对动力系统及相关主题半年度研讨会春季会议的部分（但必不可少的）支持，该研讨会自1992年以来由马里兰州和宾夕法尼亚州立大学数学系的动力学小组共同主办。（秋季会议在宾夕法尼亚州立大学举行。）会议涵盖了动力系统中广泛的主题，在大多数会议中都有一个特定的（但不是唯一的）重点领域。本次会议的目的是促进数学结果的交流；促进动力系统和相关领域的相互作用和进步；在这些范畴培养社区意识和共同使命感；并为研究生和最近的博士学位获得者的培训以及他们融入动力学社区做出贡献。特别是，在会议中间，研究生通常会有3到8个简短的演讲，效果很好。多年来，许多杰出的数学家以及（我们现在看到的）未来的领导者都参加了这次会议。过去项目的历史可以在会议网站www.math.umd.edu/research/dynamics/conferences上找到。粗略地说，动力系统领域研究系统随时间变化的方式：特别是系统的典型点随时间的变化，以及系统中感兴趣的特性在系统扰动下何时是稳定的。由于许多数学结构都可以根据它们如何随时间变化来考虑，动力系统使用了广泛的数学学科（包括微分方程、泛函分析、几何、概率论和许多其他学科）。相反，动态方法对这些领域的一些进展做出了重大贡献，在一个深刻而重要的层面上。最近的一个例子——在数论中！——是对格林和陶的工作的动态影响，他们的工作表明素数包含任意长的等差数列。此外，从动力系统的角度对各种实际问题进行了卓有成效的研究，包括目前在天气预报和空间“旅行者”轨道计算中的应用。近年来，“混沌理论”作为动力系统的一部分对科学实践产生了影响。马里兰州动力学小组成员吉姆·约克（Jim Yorke）因在这一领域的贡献而获得2003年日本奖（与Benoit Mandelbrot）。这个40万美元的奖金是世界上最负盛名的科学奖项之一。

Abstract for NSF Proposal DMS-0600296This award continues the partial (but essential) support of NSF for the spring meeting at Maryland of the Semi-annual Workshop in Dynamical Systems and Related Topics, cosponsored since 1992 by the dynamics groups in the mathematics departments of Maryland and Penn State. (The fall meeting is held at Penn State.) The conference covers a broad range of topics in dynamical systems, with a particular (but not exclusive) area of emphasis in most meetings. The goals of this conference are to promote the communication of mathematical results; to facilitate interaction and progress in dynamical systems and related fields; to nurture the sense of community and common mission in these fields; and to contribute to the training of graduate students and recent Ph.D. recipients and to their integration into the dynamics community. In particular, in the middle of the conference there are typically 3 to 8 short talks by graduate students with good results.Over the years the conference has enjoyed the participation of many prominent mathematicians, as well as (we see now) future leaders. History of past programs can be found at the conference websitewww.math.umd.edu/research/dynamics/conferences .The field of dynamical systems, roughly speaking, studies the way in which systems change over time: especially, how typical points of a system behave over time, and when properties of interest in a system are stable under perturbation of the system. Because so many mathematical structures can be considered in terms of how they change over time, dynamical systems uses a broad range of mathematical disciplines (including differential equations, functional analysis, geometry, probability theory and many others). Conversely, the dynamical approach has contributed significantly to progress in some of these fields, at a deep and nontrivial level. A recent example -- in number theory! -- is the dynamical influence on the work of Green and Tao which showed that the prime numbers contain arbitrarily long arithmetic progressions. In addition, various practical problems are fruitfully studied from the viewpoint of dynamical systems, including current applications in weather forecasting and the computation of orbits of space "voyagers". In recent years "chaos theory", a part of dynamical systems, has had an impact on scientific practice. Jim Yorke, a member of the Maryland dynamics group, shared the 2003 Japan Prize (with Benoit Mandelbrot) for his contributions in this area. This $400,000 prize is among the world's most prestigious scientific awards.