Hello everyone,

I just wanted to invite you to the final seminar of the semester. We are really happy to have Brandon Bavier from Michigan State coming to speak in our seminar. His title and abstract are below.

Title: Guts, Volume, and Skein Modules of 3-Manifolds Speaker: Brandon Bavier, Michigan State University Date: Dec 2, 2020 Time: 3:45 PM central (4:45 PM eastern) Room: Virtual meeting https://meet.google.com/frv-bgow-byi Abstract: When looking at hyperbolic alternating knots in S^3 , there is a relation between the twist number, the Jones polynomial, and the volume of the knot complement. Little is known for general hyperbolic links, or links in other manifolds. We consider hyperbolic links that admit alternating projections on surfaces in compact, irreducible 3-manifolds. Under some mild hypotheses, we are able to show that volume of the link complement is bounded below in terms of a Kauffman bracket function defined on link diagrams on the surface. Further, if the manifold is a thickened surface, we can construct a Jones-type polynomial that is an isotopy invariant that leads to a 2-sided linear bound on the volume of hyperbolic alternating links in the thickened surface

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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