Homogeneous dynamics with applications to number theory

遍历理论和群作用动力学的研究及其与数论的相互作用是一个非常活跃的研究领域。最近的重要工作艾因西德勒Katok Lindenstrass的Littlewood猜想丢番图近似和陶绿色素数在算术级数提供壮观的例子的有效性的动力学和遍历技术。该项目旨在一方面研究流形的数论性质，另一方面开发一套新的工具来研究动力系统。所解决的问题是在这个令人兴奋的跨学科领域的研究前沿。用于研究关键问题的方法将涉及现有方法的创造性应用和开发一套新工具来解决长期存在的问题。

The study of Ergodic Theory and dynamics of group actions and its interactions with number theory is an extremely active field of research. The recent important work of Einsiedler-Katok-Lindenstrass on the Littlewood conjecture in Diophantine approximation and Tao-Green on primes in arithmetics progressions offer spectacular instances of the effectiveness of dynamical and ergodic techniques. The project aims to study number theoretic properties of manifold on the one hand and develop a new set of tools in the study of dynamical systems on the other. The problems addressed are at the forefront of research in this exciting interdisciplinary area. The method used to study the key problems will involve a combination of creative applications of existing methods and the development of a new set of tools to address long standing problems.