Mdtop September 2019

mdtop@mathdept.okstate.edu

1 participants
2 discussions

No topology seminar today
by Hoffman, Neil 24 Sep '19

24 Sep '19

However, the number theory seminar today is relevant to hyperbolic geometry: Oklahoma State University Number Theory Seminar Title Binary Hermitian Forms and the Descartes Circle Theorem Speaker: David Wright, OSU Date: Sep 24, 2019 Time: 3:30 PM Room: MSCS 422 Abstract: Recently, there has been a lot of interest in Apollonian circle packings where the curvatures turn out to be integers, and the properties of the integers that occur as curvatures. We shall reframe this in terms of the binary hermitian forms corresponding to generalized circles and use that theory to derive the Descartes Four Circle Theorem, and similar theorems for other Kleinian circle packings. We shall use this to prove the curvatures in other Kleinian circle packings are algebraic integers in certain number fields. ______________________ 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

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Will Worden today
by Hoffman, Neil 10 Sep '19

10 Sep '19

Hello everyone, Today at 3:30 we have Will Worden speaking in seminar. The talk details are below. Title: Small knots of large Heegaard genus Speaker: Will Worden, Rice University Date: Sep 10, 2019 Time: 3:30 PM Room: MSCS 509 Abstract: Building off ideas developed by Agol, we construct a family of hyperbolic knots Kn whose complements contain no closed incompressible surfaces (i.e., they are small) and have Heegaard genus exactly $n$. These are the first known examples of small knots having large Heegaard genus. In the first part of the talk we will describe a beautiful construction due to Agol for building hyperbolic 3-manifolds that decompose into a union of regular ideal octahedra. Using this technology, we will then show how to build the knots Kn, and outline the proof showing that they have the desired properties ______________________ 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

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Mdtop September 2019