Title: The morse boundary determines CAT(0) groups up to quasi-isometry
Speaker: Devin Murray (Brandeis University)
Abstract: The boundary of hyperbolic space is an important invariant in classical hyperbolic geometry and it plays a pivotal role in many rigidity theorems. The Gromov boundary has played a similar role in the study of delta-hyperbolic groups. In particular, the Gromov boundary of a delta hyperbolic group determines the group up to quasi-isometry type. While CAT(0) spaces also have a notion of a boundary, the topological type of this boundary is not a quasi-isometry invariant and is therefor not well defined for a CAT(0) group. This is where the morse boundary for CAT(0) groups comes in. It was introduced by Charney and Sultan who showed that it is a QI invariant and thus a well defined notion for a CAT(0) group. The morse boundary, equipped with some extra data, completely determines a CAT(0) group. I will talk about the ingredients needed to prove this fact and time permitting I will discuss some about how this fits into other questions about QI rigidity.