Mathematics Colloquium
Nick Miller
UC Berkeley
Title: Geodesic submanifolds and arithmeticity
Date: Wednesday, January 26, 2022
Place and Time: Zoom, 3:05-3:55 pm
Abstract.
Constructions of hyperbolic manifolds naturally divide themselves into two classes - "arithmetic" and "non-arithmetic". The former arise naturally from certain number theoretic constructions however, due to this, the geometry of the subsequent manifold is rather mysterious. In this talk, I will survey our current understanding of arithmetic and non-arithmetic hyperbolic manifolds in all dimensions, discuss known constructions, and then conclude by explaining recent results that give a geometric characterization of arithmeticity using geodesic submanifolds.