A Dynamical Systems Weekend Conference at Wesleyan

该奖项将支持将于2020年4月4日至5日在康涅狄格州米德尔敦卫斯理大学举行的会议的参与者。这次会议的主题是动力系统。将有12位主讲嘉宾，其中包括早期职业数学家，特别是研究生和博士后学者。起源于数学和计算机科学各个领域的一些重要问题可以用动力系统来研究。粒子在空间中的运动是由一个函数的作用或空间的变换来模拟的。后来的数学家考虑了几个这样的函数，它们被放在一组变换中，并研究了所谓的群作用。卫斯理会议的目标是将各种研究人员和学生聚集在一起，他们的工作与动力学中的群体行为研究有关，讨论最新的研究成果，并寻求合作来解决这一领域的开放性问题。齐次动力学已被证明是数论和几何研究的有力工具。虽然在许多情况下，定性结果已经足够应用，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。它通常涉及对涉及群体在空间上行动的各个方面的比率或误差项进行估计。会议将讨论齐次动力学中有效均匀分布和收缩目标的最新进展，并研究这些结果如何有助于促进对数论问题的理解。会议的另一个主要主题是动力学系统的行为建模，一个球在多边形内弹跳。这一研究课题在代数几何、几何中的刚性理论、Teichmuller理论和其他数学领域中发现了令人兴奋的联系和应用。会议将主持关于这一方向的最新工作的讨论，并讨论它们在平铺几何、平移表面、间隔交换变换和相关主题中的应用。会议还将包括概率论和群上的随机漫步、幂零群的几何、标记长度谱和表面刚性等方面的研究。它将为研究生提供一个接触现代动力系统理论的不同视角并与会议参与者交流的绝佳机会。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，认为值得支持。

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.