Mathematical Sciences: Supplement To: Ergodic Theory, Groupsand Geometry - Differential Geometry and Dynamical Systems by: Renato Feres

Feres将研究微分几何和动力系统中的几个问题，其目的是理解群作用的某些刚性现象。这些问题的解可以对Zimmer关于高阶格群作用的一般猜想有所启发，并在特殊情况下改进Gromov关于刚性变换群的理论，当刚性变换群具有定义具有双曲行为的动力系统的元素时。​这个项目涉及遍历理论的研究。遍历理论一般关注理解系统的平均行为，其动力学过于复杂或混乱，无法在微观细节上进行跟踪。在“动力学”的标题下，可以放置关于抽象变换如何作用于光滑空间的现代理论。通过这种方式，遍历理论在寻求对均匀空间上的流动进行分类时与几何联系在一起。

Feres will study several problems in differential geometry and dynamical systems whose aim is to understand certain phenomena of rigidity of group actions. The solution to these problems could shed some light on a general conjecture of Zimmer's concerning actions of higher rank lattice groups and improve certain aspects of Gromov's theory of rigid transformation groups in the special case when such groups possess elements that define dynamical systems with hyperbolic behavior. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.