Topology Seminar (Main Talk): Discrete isometry groups of higher rank symmetric spaces

Seminar | September 20 | 4-5 p.m. | 3 Evans Hall

 Misha Kapovich, UC Davis

 Department of Mathematics

I will review basic geometry of higher rank symmetric spaces, and then discuss discrete isometry groups of such spaces, which are higher rank generalizations of Kleinian groups. We will see how some of the classical notions and results translate in the higher rank setting and how do they connect to the broader geometric group theory. For instance: What is the higher rank analogue of the convergence property for Moebius transformations? How to define limit sets and domains of discontinuity in higher rank? How to define geometrically finite discrete groups in higher rank? What could quasiconvexity mean? Why would a person interested in RAAGs care about any of this? The talk is based on my work with Bernhard Leeb and Joan Porti.