Fun with finite covers of 3-manifolds: connections between topology, geometry and arithmetic

Friday, February 24, 2017 - 15:30
704 Thackeray
Speaker Information
Nathan Dunfield
University of Illinois at Urbana-Champaign

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Abstract or Additional Information

From the revolutionary work of Thurston and Perelman, we know the topology of 3-manifolds is deeply intertwined with their geometry. In particular, hyperbolic geometry, the non-Euclidean geometry of constant negative curvature, plays a central role. In turn, hyperbolic geometry opens the door to applying tools from number theory, specifically automorphic forms, to what might seem like purely topological questions.

After a passing wave at the recent breakthrough results of Agol, I will focus on exciting new questions about the geometric and arithmetic meaning of torsion in the homology of finite covers of hyperbolic 3-manifolds, motivated by the recent work of Bergeron, Venkatesh, Le, and others. I will include some of my own results in this area that are joint work with F. Calegari and J. Brock.

 

 

HOST: Jason DeBlois

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