Due to the COVID-19 Pandemic, the University has instruction to cancel all in-person events through the Fall semester to adhere to city and state orders limiting public gatherings. Events still running must now take place Online— listed events will include a link in which one may access the Online webspace:

To view Prof. Healys’ talk, enter his Online chatroom via Microsoft Teams— it will open on Monday, December 7th, 2020.

Homogeneous Spaces not Admitting Geometric (quasi)-actions

Prof. Burns Healy

University of Wisconsin-Milwaukee

Professor, Department of Mathematical Sciences

“Thurston’s geometrization answers the question of what homogeneous Riemannian manifolds occur as the universal cover of a closed 3-manifold. The “reverse” question is also of interest; that is, when does a given homogeneous Riemannian manifold cover a finite volume quotient? When the upstairs space is strictly negatively curved, there is a complete classification of this behavior due to Heintze. In this talk, we will examine a generalization of these Heintze spaces (negatively curved homogeneous Riemannian manifolds), a particular class of solvable Lie groups which admit CAT(0) metrics. We give a characterization of when these metric spaces admit finite volume quotients. Furthermore, we produce a wide array of examples of these spaces which do not admit any geometric quasi-actions by discrete groups, meaning they are cocompact but not QI to any discrete group. This talk represents joint work with Mark Pengitore.”