## Geometry, Topology and Dynamics Seminar

Carolyn Abbott

University of Wisconsin, Madison

Universal acylindrical actions

**Abstract:**Given a finitely generated group, one can look for an acylindrical action on a hyperbolic space in which all elements that are loxodromic for some acylindrical action of the group are loxodromic for this particular action. Such an action is called a universal acylindrical action and, for acylindrically hyperbolic groups, tends to give a lot of information about the group. I will discuss recent results in the search for universal acylindrical actions, describing a class of groups for which it is always possible to construct such an action as well as an example of a group for which no such action exists.

Monday February 27, 2017 at 3:00 PM in SEO 636