Hello everyone,

Tomorrow we have Nicholas Rouse joining us from Rice. We will meet in the usual place: https://meet.google.com/frv-bgow-byi

His title and abstract are below:

Title: Arithmetic invariants of Dehn surgery points Speaker: Nicholas Rouse, Rice University Date: Mar 17, 2021 Time: 3:30 PM Room: https://meet.google.com/frv-bgow-byi Abstract: Associated to an orientable, finite volume hyperbolic 3-orbifold is a number field and a quaternion algebra over that field. Such quaternion algebras are classified up to isomorphism by their ramification sets, which is a finite set of prime ideals and embeddings into the real numbers. Chinburg, Reid, and Stover show that orbifolds obtained by Dehn surgery on knots whose Alexander polynomial satisfies some condition have quaternion algebras ramifying above a finite number of rational primes. However, computer experiment suggests that knots that do not satisfy this Alexander polynomial condition have surgeries ramifying above infinitely many distinct primes. We prove this is the case for a family of twist knots and one knot not in that family