A Dynamical Systems Weekend Conference at Wesleyan

卫斯理学院动力系统周末会议

• 批准号: 2000176
• 负责人: Han Li
• 金额: $ 0.6万
• 依托单位: Wesleyan University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-03-01 至 2023-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2000176&HistoricalAwards=false
• 关键词: Dynamical; Systems; Weekend; Conference; Wesleyan

This award will support participants in a conference to be held at Wesleyan University in Middletown, Connecticut on April 4-5, 2020. The conference is in the area of dynamical systems. There will be twelve main speakers, and will include early career mathematicians, especially graduate students and post-doctoral scholars. Several important problems originating from various fields in mathematics and computer science can be studied in terms of dynamical systems. The motion of a particle in space has been modeled by the action of a function or transformation of the space. Later mathematicians considered several such functions that were put together in group of transformations and studied what are called group actions. The goal of the conference at Wesleyan is to bring together a variety of researchers and students whose work connects to the study of group actions in dynamics to discuss the latest research findings and to seek collaborations to attack open problems in this area. Homogeneous dynamics has proven to be a powerful tool in the study of number theory and geometry. Although in many cases qualitative results already suffice for applications, there are situations in which it is essential to obtain effective, quantitative results in homogenous dynamics. It usually involves giving estimates on the rates or error terms which concern various aspects of group actions on spaces. The conference will discuss recent progress on effective equi-distribution and shrinking targets in homogeneous dynamics, and study how these results could help advance the understanding of problems in number theory. Another main topic of the conference is the behavior of dynamical systems modeling a ball bouncing around inside a polygon. This research subject has found exciting connections and applications to algebraic geometry, rigidity theory in geometry, Teichmuller theory, and other areas of mathematics. The conference will host talks on recent works in this direction and discuss their applications to the geometry of tiling, translation surfaces, interval exchange transformations, and related topics. The conference will also include research talks in probability theory and random walks on groups, geometry of nilpotent groups, marked length spectrum, and rigidity of surfaces. It will provide a great opportunity for graduate students to be exposed to different perspectives of the modern theory of dynamical systems and to communicate with conference participants. The conference website is https://dynamicalweekend.conference.wesleyan.edu/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项将支持2020年4月4日至5日在康涅狄格州米德尔敦的卫斯理大学举行的会议的参与者。会议位于动态系统领域。将有十二位主演讲者，其中包括早期的职业数学家，尤其是研究生和博士后学者。可以根据动态系统研究数学和计算机科学领域的各个领域的几个重要问题。粒子在空间中的运动是通过函数或空间转换的作用来建模的。后来的数学家考虑了几个这样的功能，这些功能被整合在一起，并研究了所谓的小组行动。卫斯理人会议的目标是将各种研究人员和学生汇集在一起​​，他们的工作与动态中的小组行动有关，以讨论最新的研究结果，并寻求合作以攻击该领域的开放问题。事实证明，同质动力学是数字理论和几何学研究中的强大工具。尽管在许多情况下，定性结果已经足够用于应用，但在某些情况下，必须在同质动力学中获得有效的定量结果。它通常涉及对涉及空间小组行动各个方面的速率或错误条款进行估算。会议将讨论有关有效的等值分布和均匀动态目标缩小目标的最新进展，并研究这些结果如何帮助提高对数量理论问题的理解。会议的另一个主要主题是动态系统的行为，建模多边形内部的球弹跳。该研究主题发现了与代数几何形状，几何形状，Teichmuller理论和其他数学领域的僵化理论的令人兴奋的联系和应用。该会议将朝着这个方向进行有关最新作品的谈判，并讨论他们对平铺，翻译表面，间隔交换转换和相关主题的几何形状的应用。该会议还将包括概率理论的研究谈判和对群体的随机步行，尼尔疗法群体的几何形状，明显的长度频谱和表面的刚度。它将为研究生提供一个很好的机会，以接触现代动态系统理论的不同观点，并与会议参与者进行沟通。会议网站是https://dynamicalweekend.conference.wesleyan.edu/this Award反映了NSF的法定任务，并且使用基金会的知识分子优点和更广泛的影响审查标准，被认为值得通过评估来获得支持。