Wednesday, 14 November 2018
Damian Sawicki: On metric spaces defined by group actions
One approach to study infinite groups is to treat them as geometric objects. In the talk we will refine this approach by associating a geometric object to an action on a compact space.The geometry of the associated invariant turns out to reflect topological and ergodic properties of the action (amenability, Haagerup propery, spectral gap) and may even remember the action completely (Fisher et al.), but it may also not distinguish between actions of the integers and of the trivial group (joint work with Kielak).
The construction also yields exotic examples of interest in computer science and large scale geometry (super-expanders and counterexamples to the coarse Baum–Connes conjecture).