University of Maryland Spring Dynamics Conference

NSF提案DMS-0600296摘要该奖项延续了NSF对马里兰州春季会议的部分（但必不可少的）支持，该会议是自1992年以来由马里兰州和宾夕法尼亚州数学系动力学小组共同主办的动力系统和相关主题的半年研讨会。(The秋季会议在宾夕法尼亚州立大学举行。）会议涵盖了广泛的主题在动力系统，与一个特定的（但不是唯一的）领域的重点在大多数会议。本次会议的目标是促进数学成果的交流;促进动力系统及相关领域的互动和进步;培养这些领域的社区意识和共同使命;并为培养研究生和最近的博士生做出贡献。接受者和他们融入动态社区。特别是，在会议的中间通常有3到8个简短的演讲，由研究生取得了良好的效果。多年来，会议一直享有许多杰出的数学家的参与，以及（我们现在看到）未来的领导者。过去项目的历史可以在会议websitewww.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如何随着时间的推移而表现，以及系统中感兴趣的属性何时在系统扰动下保持稳定。 由于许多数学结构可以根据它们如何随时间变化来考虑，因此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，概率论等）。相反，动力学方法在这些领域中的一些领域中，在深层次和非平凡的水平上做出了重大贡献。最近的一个例子--在数论中！--是动态的影响工作的绿色和陶其中表明，素数包含任意长的算术级数。此外，从动力系统的观点出发，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，作为动力系统的一部分，“混沌理论”对科学实践产生了影响。马里兰州动力学小组的成员吉姆·约克（Jim Yorke）因其在这一领域的贡献而与贝努瓦·曼德尔布罗特（Benoit Mandelbrot）分享了2003年日本奖。这个40万美元的奖项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.