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Differential Geometry: "Geodesics Subspaces in Arithmetic Hyperbolic 3-Manifolds”

Dr. Jeffrey Meyer, CSUSB

Friday, March 17, 2017
  11:10 a.m.–Noon

Location: Surge Building 268
  Parking Information

Category: Seminar


Standard arithmetic hyperbolic manifolds exhibit rich collections of totally geodesic subspaces. The collections of these subspaces contain a great deal of information. For example, the commensurability class of an arithmetic hyperbolic 3-manifolds is completely determined by the set of lengths of closed geodesics, or alternatively by the set of its totally geodesic surfaces. In this talk I will give a gentle introduction of the theory of arithmetic hyperbolic 3-manifolds and explain how manifolds, their surfaces and their geodesics relate to division algebras, their subalgebras, and their maximal subfields. I will then discuss recent work with collaborators in which we leverage number theoretic techniques to construct and count hyperbolic manifolds exhibiting specified subspace conditions.

Additional Information: Math Seminars

Open to: General Public
Admission: Free
Sponsor: Mathematics

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