Dynamical Developments: A Conference in Complex Dynamics and Teichmuller Theory

该奖项支持美国研究人员参加2015年8月17-21日在德国不来梅雅各布斯大学举行的国际会议“动态发展：复杂动力学和泰希米勒理论会议”。动力系统在我们周围无处不在：行星的运动、天气、股票市场和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，将动力系统及其相应的参数空间复杂化，即将显著的量视为复数而不是(更受限制的)实数，会为研究潜在的数学问题带来新的见解和工具。复杂动力学是一个非常活跃的领域，在过去的几十年里经历了巨大的进步。这次会议将汇集不同的参与者群体，从这些领域的不同专家到开始研究的年轻研究人员，举行一次紧张而集中的会议，讨论这一主题令人兴奋的新发展、想法和方向。复杂动力学在过去25年中蓬勃发展。这一发展阶段导致了对某些单参数模型族(例如，二次多项式)的深入研究。这门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Teichmüler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、双曲和代数几何以及统计物理。会议将由复杂动力学和泰希米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，这次会议还将有两个与目前的数学会议不太常见的方面：将有一个青年研究人员研讨会，在研讨会上，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；以及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

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