Due to the COVID-19 Pandemic, the University has instruction to cancel all in-person events through the Spring 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 Dr. Patel’s talk, enter her Online chatroom via Microsoft Teams— it will open at 3:00pm on Friday, March 5th, 2021.

Quantitative methods in hyperbolic geometry

Dr. Priyam Patel
Assistant Professor of Mathematics
University of Utah

“Peter Scott’s famous result states that the fundamental groups of hyperbolic surfaces are subgroup separable, which has many important and non-trivial consequences. For example, given any closed curve on such a surface, potentially with many self-intersections, there is always a finite cover to which the curve lifts to an embedding. It was shown recently that hyperbolic 3-manifold groups share this separability property, and this was a key tool in Agol’s recent resolution to the Virtual Haken and Virtual Fibering conjectures for hyperbolic 3-manifolds.

I will begin this talk by giving some background on separability properties of groups, hyperbolic manifolds, and these two conjectures. There are also a number of interesting quantitative questions that naturally arise in the context of these topics. These questions fit into a recent trend in low-dimensional topology aimed at providing concrete topological and geometric information about hyperbolic manifolds that often cannot be gathered from existence results alone. I will highlight a few of them before focusing on a quantitative question regarding the process of lifting curves on surfaces to embeddings in finite covers.”

*Click to view the event flyer.