Dynamical Developments: A Conference in Complex Dynamics and Teichmuller Theory

动力学发展：复杂动力学和泰希米勒理论会议

• 批准号: 1500750
• 负责人: Sarah Koch
• 金额: $ 5万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-01 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1500750&HistoricalAwards=false
• 关键词: Dynamical; Developments; Conference; Complex; Dynamics

This award supports the participation of U.S.-based researchers in the international conference "Dynamical Developments: A Conference in Complex Dynamics and Teichmüller theory," taking place August 17-21, 2015, at Jacobs University in Bremen, Germany. Dynamical systems are all around us: the motion of the planets, the weather, the stock market, and the ecosystems in which we live. These systems depend on a variety of parameters, and as these parameters change, the corresponding system is affected. Often, "complexifying" a dynamical system and its corresponding parameter space, that is, regarding the salient quantities as complex numbers rather than (the more highly restricted) real numbers, leads to new insights and tools for investigating the underlying mathematics. Complex dynamics is a very active field that has experienced tremendous progress over the past few decades. This conference will bring together a diverse group of participants, ranging from various experts in these fields to younger researchers who are beginning their studies, for an intense and focused meeting to discuss exciting new developments, ideas, and directions for the subject.Complex dynamics has thrived over the past 25 years. This period of development has led to deep results on certain one-parameter model families (quadratic polynomials, for example). The time is ripe for the subject to advance to a more general theory, which will inevitably involve related fields such as Teichmüller theory, moduli spaces, dynamics in several complex variables, self-similar groups, arithmetic dynamics, symbolic dynamics, hyperbolic and algebraic geometry, and statistical physics. The conference will feature presentations by leading experts in complex dynamics and Teichmüller theory and will provide ample time for discussions. In addition to the formal scientific program, this conference will have two aspects less common to current mathematics conferences: there will be a young researchers seminar in which more junior participants can share their work with the community of mathematicians attending the conference, and there will be a computer program tutorial, showcasing some of the latest software used in the field. Conference web site : http://www-personal.umich.edu/~kochsc/H70.html

该奖项支持美国研究人员参加2015年8月17日至21日在德国不来梅雅各布斯大学举行的国际会议“动力学发展：复杂动力学和teichmller理论会议”。动力系统就在我们身边：行星的运动、天气、股票市场以及我们生活的生态系统。这些系统依赖于各种参数，随着这些参数的变化，相应的系统也会受到影响。通常，“复杂化”一个动力系统及其相应的参数空间，也就是说，将显著量视为复数而不是（更严格限制的）实数，会为研究基础数学带来新的见解和工具。复杂动力学是一个非常活跃的领域，在过去的几十年里取得了巨大的进步。本次会议将汇集不同群体的参与者，从这些领域的不同专家到刚刚开始研究的年轻研究人员，这是一个紧张而集中的会议，讨论令人兴奋的新发展、想法和方向。在过去的25年里，复杂动力学蓬勃发展。这一时期的发展导致了对某些单参数模型族（例如二次多项式）的深入研究。该学科发展到更一般理论的时机已经成熟，这将不可避免地涉及到相关领域，如teichm<s:1> ller理论、模空间、多复变量动力学、自相似群、算术动力学、符号动力学、双曲几何和代数几何以及统计物理。会议将由复杂动力学和teichm<e:1>勒理论方面的主要专家发表演讲，并将提供充足的讨论时间。除了正式的科学计划外，本次会议将有两个与当前数学会议不同的方面：将有一个年轻研究人员研讨会，更多的初级参与者可以与参加会议的数学家社区分享他们的工作，并将有一个计算机程序教程，展示该领域使用的一些最新软件。会议网址：http://www-personal.umich.edu/~kochsc/H70.html