EVENT DETAILS AND ABSTRACT

Title: Uniform versus non-uniform convergence action on the two-sphere
Speaker: Daniel Groves
Speaker Info: University of Illinois at Chicago
Brief Description:
Special Note: Midwest Dynamical Systems Conference
Abstract:

The Cannon conjecture states that if a group G acts as a uniform convergence group on the two-sphere then (up to finite groups) G is a cocompact Kleinian group and that the G-action is topologically conjugate to an action on the two-sphere by Mobius transformations. Thus, it predicts that a dynamical condition with no smoothness conditions can be upgraded to a conformal action.

I will begin by explaining what a uniform convergence group action is, and the natural generalization to the non-uniform setting, where there is a version of the Cannon Conjecture. I will explain joint work with Jason Manning and Alessandro Sisto that the uniform version implies the non-uniform version. Time permitting, I will describe work in preparation with Manning, Sisto and also Damian Osajda and Genevieve Walsh that (under mild hypotheses) proves the converse implication.