CAREER: Rigidity of Group Actions in Ergodic Theory and Geometry

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AbstractFurmanThe research component of the project concerns with various aspects ofrigidity in Ergodic theory, Lie groups and Hyperbolic Geometry. Thecommon theme of the proposed research projects is the analysis of group actions on spaces endowed with a measurable, topological or geometrical structure. More specifically, in the context of ErgodicTheory the proposed problems address the structure and invariants of ergodic equivalence relations on probability spaces generated bymeasurable actions of lattices in Lie groups. In the context ofHyperbolic geometry the goal is to study negatively curved Riemannian structures on compact manifolds through coarse-geometric point ofview on the fundamental group.Generally, the research component of the project is focused on dynamics and geometry of various systems which have a rich groupof symmetries in the search of special phenomena occurring due tothese symmetries. The educational component of the project is aimed to contribute to the graduate studies program via special designed Workshop in Mathematics Seminar and advanced Topic courses. The goal is to engage students in small scale "self discovery" projects via sets of challenging problems, to encourage independent thinking and to expose students to a wide spectrum of current research.