2017 Pingree Park Dynamical Systems School

2017 年 Pingree Park 动力系统学校

• 批准号: 1700430
• 负责人: Nicholas Ormes
• 金额: $ 2.5万
• 依托单位: University of Denver
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-03-01 至 2018-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1700430&HistoricalAwards=false
• 关键词: 2017; Pingree; Park; Dynamical; Systems

The Pingree Park Dynamical Systems School will take place at the Pingree Park Campus of Colorado State University, CO on the dates July 16-21, 2017. A group of 36 research mathematicians will be brought together to discuss problems in dynamical systems, focused mainly on problems related to symbolic dynamics. There will be three extended mini-courses on exciting new research presented by three well-known experts in this field. In addition, sixteen other 30 minute talks will be presented by conference participants. Participants will include graduate students, postdocs as well as more senior researchers. The organizer will conduct a one hour "problem session" in which participants pose open problems in the area to stimulate discussion throughout the conference. The goal of the meeting is to bring together researchers working in different, but closely related, fields to disseminate results and initiate new lines of inquiry. As with the successful 2014 Pingree conference, the meeting participants will include a heavy proportion of young researchers who, through the mini-courses, can both learn foundational material and be brought up to speed on new developments. The Pingree Park Campus provides an ideal environment for interaction and thoughtful investigation, fostering research and development in this broad area of research. The main topic of this meeting will be group actions on zero-dimensional spaces, but related fields in dynamics will also be represented. The conference will revolve around three mini-courses, given by experts on the main topics of the meeting. Much recent activity on symbolic dynamics of general group actions centers on some unexpected connections to computability theory and algorithmic complexity. Emmanuel Jeandel is a world-renowned researcher in this area and his mini-course should provide a useful introduction, and describe current fertile directions for research. For Z-actions, symbolic dynamics is a standard tool for modeling more general systems, but similar techniques for more general group actions are still not well-understood. Anthony Quas and Ayse Sahin have done significant work of this sort, including a multidimensional version of Rokhlin's Lemma and hypotheses guaranteeing existence of Markov partitions for multidimensional systems. At least one of their minicourses will pertain to some of this work, and that the other may relate to some of their other excellent work, such as Sahin's work on actions of the Heisenberg group or Quas's work on relative maximal entropy.

Pingree Park动态系统学校将于2017年7月16日至21日在科罗拉多州立大学的Pingree Park校区举行。一组36名研究数学家将聚集在一起讨论动力系统中的问题，主要集中在与符号动力学有关的问题。将有三个扩展的迷你课程，由该领域的三位知名专家介绍令人兴奋的新研究。此外，与会者还将发表16场30分钟的演讲。参与者将包括研究生，博士后以及更高级的研究人员。组织者将进行一个小时的“问题会议”，与会者提出该地区的开放性问题，以激发整个会议的讨论。会议的目标是将在不同但密切相关的领域工作的研究人员聚集在一起，传播成果并启动新的调查路线。与2014年成功举办的Pingree会议一样，与会者将包括大量年轻研究人员，他们通过小型课程既可以学习基础材料，又可以加快新的发展。Pingree Park校区为互动和周到的调查提供了理想的环境，促进了这一广泛研究领域的研究和发展。 本次会议的主要议题将是零维空间上的群作用，但也将代表动力学的相关领域。会议将围绕三个小型课程进行，由专家就会议的主要议题授课。最近关于一般群体作用的符号动力学的许多活动集中在与可计算性理论和算法复杂性的一些意想不到的联系上。Emmanuel Jeandel是这一领域的世界知名研究人员，他的迷你课程应该提供有用的介绍，并描述当前的研究方向。对于Z-行动，符号动力学是一个标准的工具，用于建模更一般的系统，但类似的技术，更一般的群体行动仍然没有得到很好的理解。安东尼·奎斯和艾塞·沙欣在这方面做了大量的工作，包括罗克林引理的多维版本和保证多维系统马尔可夫分割存在的假设。至少有一个他们的minicourses将涉及到一些这项工作，而其他可能涉及到一些其他优秀的工作，如沙欣的工作行动的海森堡集团或夸斯的工作相对最大熵。