Title: Arithmetic of Dehn surgery points and Azumaya algebras

Date: 10/26/2017

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Speaker: Alan Reid, Rice University

Associated to a finite volume hyperbolic 3-manifold is a
number field and a quaternion algebra over that number field. Closed hyperbolic 3-manifolds arising from Dehn surgeries on a hyperbolic knot complement provide a family of number fields and quaternion algebras that can be viewed as "varying" over a certain curve component (the so-called canonical component) of the SL(2,C)-character variety of the knot group. This talk will give examples of different behavior and survey recent work on how the varying behavior can be explained using the language of Azumaya algebras over the canonical curve.