We'll introduce the WPD property for groups, which can be thought of as a discreteness property for the action of a group on a space which need not be locally compact. More precisely, the action of a group on a Gromov hyperbolic space X is WPD if the action is coarsely discrete along the quasi-axis of a loxodromic isometry. We'll give some examples of WPD groups, which include the mapping class group of a surface and Out(F_n), and consider when the action of a group on a quotient of X might still satisfy the WPD property. We'll also show that WPD elements are generic for random walks on WPD groups. This includes joint work with Hidetoshi Masai, Saul Schleimer and Giulio Tiozzo.
Join Zoom meeting ID 613 8691 2732 or via the link below.
Passcode: A group is called an ________ group if it admits an invariant mean. (8 letters, lowercase)