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Department of Computer Science at Lehman College

Department News

Spring 2019

Professor Owen Recognized with Prestigious Early Career Award

Megan Owen, an assistant professor in the Department of Mathematics at Lehman College, has earned one of the most prestigious career advancement awards offered by the National Science Foundation (NSF). Read more about the news.

Fall 2018

Title: Quantitative methods in Hyperbolic Geometry

Abstract: Peter Scott’s famous result states that the fundamental groups of hyperbolic surfaces are subgroup separable, which has many powerful 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 Ian Agol's 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.