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.
