Dynamical Developments: A Conference in Complex Dynamics and Teichmuller Theory

该奖项支持美国的参与-基于研究人员在国际会议“动态发展：在复杂动力学和Teichmüller理论会议”，发生在2015年8月17日至21日，在雅各布斯大学在不莱梅，德国。动力系统就在我们周围：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，并且当这些参数改变时，相应的系统受到影响。通常，“复杂化”一个动力学系统及其相应的参数空间，也就是说，把显着的量看作复数，而不是（更严格限制的）真实的数，这会带来新的见解和工具来研究基础数学。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展。本次会议将汇集来自不同领域的专家和刚开始研究的年轻研究人员，以一个紧张而有重点的会议来讨论该主题令人兴奋的新发展，想法和方向。复杂动力学在过去的25年中蓬勃发展。这一时期的发展导致了某些单参数模型族（例如二次多项式）的深入结果。时机已经成熟的主题推进到一个更普遍的理论，这将不可避免地涉及相关领域，如泰希米勒理论，模空间，动力学在几个复杂的变量，自相似群体，算术动力学，符号动力学，双曲和代数几何，统计物理。会议将由复杂动力学和Teichmüller理论的领先专家进行演讲，并将提供充足的讨论时间。 除了正式的科学计划，本次会议将有两个方面不太常见，目前的数学会议：将有一个年轻的研究人员研讨会，其中更多的初级参与者可以分享他们的工作与社会的数学家参加会议，将有一个计算机程序教程，展示一些最新的软件在该领域使用。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