Statistical and Number-Theoretical Aspects of Dynamical Systems

我的研究计划包括几个项目，涉及动力学、概率论、遍历理论、数论和数学物理的交叉学科。我的主要目标有两个：我计划了解大类动力系统的长期行为，以解决动力学和遍历理论中的开放问题，同时我打算探索新的动力学工具在其他学科中解决问题的应用，从而开发一个动力学框架来研究动力学领域以外的几个数学对象。

My research program consists of several projects at the crossroad of dynamics, probability theory, ergodic theory, number theory, and mathematical physics. My broad aim is two-fold: I plan to understand the long-time behaviour of large classes of dynamical systems to address open questions in dynamics and ergodic theory, and at the same time I intend to explore the applications of novel dynamical tools to solve problems in other disciplines, thus developing a dynamical framework to study several mathematical objects outside the realm of dynamics.