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
Hello everyone,
Today in seminar we are very happy to have Jeff Meyer joining us from Cal State - San Bernadino. His title and abstract are below. The link for seminar is the same:
https://meet.google.com/frv-bgow-byi
Title: Systoles of Arithmetic Manifolds
Speaker: Jeff Meyer, Cal State San Bernardino
Date: Mar 10, 2021
Time: 3:30 PM
Room: Virtual
Abstract: Pick your favorite compact space. How short is the shortest closed loop on it? Now look at your favorite cover of this space. Did that loop unwrap to a longer loop? These are systole questions. The systole of a manifold is the minimal length of a non-contractible closed loop. Systoles in arithmetic manifolds have many fascinating relationships with deep problems in number theory, such as Lehmer’s Mahler measure problem. In recent years, there have been numerous papers studying systoles, their bounds, and their growth up covers as you vary the underlying manifolds. In this talk, I will discuss interesting systole problems, survey known results, and present recent work with collaborators Sara Lapan and Benjamin Linowitz.
______________________
Neil R. Hoffman
Assistant Professor
Department of Mathematics
523 Math Science Building
Oklahoma State University
Stillwater, OK 74078-1058
405-744-7791
http://math.okstate.edu/people/nhoffman
Dear mdtop,
This week we have Hannah Turner visiting us (virtually) from the University of Texas.
Her title and abstact are below. As always the google meet link is:
https://meet.google.com/frv-bgow-byi
Speaker: Hannah Turner, University of Texas
Time: Wednesday, March 3, 2021, 3:30.
Title: Branched cyclic covers and L-spaces
Abstract: A 3-manifold is called an L-space if its Heegaard Floer homology is ”simple.” No characterization of all such ”simple” 3-manifolds is known. Manifolds obtained as the double-branched cyclic cover of a knot in the 3-sphere give many examples of L-spaces. In this talk, I’ll discuss the search for L-spaces among higher index branched cyclic covers of knots. In particular, I’ll give new examples of knots whose branched cyclic covers are L-spaces for every index n. This is joint work with Ahmad Issa.
______________________
Neil R. Hoffman
Assistant Professor
Department of Mathematics
523 Math Science Building
Oklahoma State University
Stillwater, OK 74078-1058
405-744-7791
http://math.okstate.edu/people/nhoffman
