When
3 – 4 p.m., March 30, 2026
Where
Title: Number Theoretic Methods for Hyperbolic 3-Manifolds
Abstract: Geodesics are an important concept in differential geometry. Generally speaking, it is possible to have closed geodesics, and naturally a question arises. Does the geodesic intersect itself before it completes its path? Such a geodesic is called non-simple. In this talk, we will explore a construction of real hyperbolic 3-manifolds all of whose closed geodesics are simple. Almost all of the techniques used are number theoretic in nature, utilizing quaternion algebras formed over number fields or (characteristic 0) number fields.