Mathematical Sciences: Manifolds of Nonpositive Curvature and Rigidity Theory

拉尔夫·斯帕齐尔将对几何和动力系统的界面进行研究。这个项目的一个中心主题是对刚性的研究。他将研究非正曲率空间的刚性性质和半单群及其格的作用。这涉及到几何学以及遍历理论和群论的问题。这些问题分为三类：高阶空间、一阶流形和群作用的刚性。

Ralf Spatzier will carry out research on the interface of geometry and dynamical systems. A central theme of this project is the study of rigidity. He will study rigidity properties of spaces of nonpositive curvature and actions of semisimple groups and their lattices. This involves problems from geometry as well as ergodic theory and group theory. The problems fall into three categories: spaces of higher rank, rank one manifolds and rigidity of group actions.