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247 discussions

Today in Seminar
by Hoffman, Neil 08 Oct '19

08 Oct '19

We have Andrew Yarmola visiting. His title and abstract are below. See you there. Title: Volumes and filling collections of simple multicurves Speaker: Andrew Yarmola, Princeton University Date: Oct 8, 2019 Time: 3:30 PM Room: MSCS 509 Abstract: Consider a link L in the trivial circle bundle N over a surface S of negative Euler characteristic. If the fiber-wise projection of L to S is a collection C of closed curves in minimal position, then N L is hyperbolic if and only if C is filling and N L is acylindrical. We would like to understand the behavior of vol(N L) in terms of the topology of C. When C is a composed of simple closed curves and L is stratified, as we will define, we show that vol(N L) is quasi-isometric to expressions involving distances in the pants graph. When S is a punctured torus or a four punctured sphere and N = P T1 (S), we show that the tangent field lift of C is always stratified and that the volume is quasi-isometric to curve complex distance. In this talk, we will outline our proofs and give several natural examples of stratified links. This is joint work with T. Cremaschi and J. A. Rodriguez-Migueles. ______________________ 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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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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Re: [Mdtop] Hyperbolic Saturdays
by Hoffman, Neil 15 Aug '19

15 Aug '19

Hi topologists, Jing Tao asked me to pass this along to our group. Best, Neil ______________________ 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 ________________________________ From: jing tao <jing(a)ou.edu> Sent: Thursday, August 15, 2019 4:33:06 PM To: Hoffman, Neil <neil.r.hoffman(a)okstate.edu>; maktas(a)uco.edu <maktas(a)uco.edu> Subject: Hyperbolic Saturdays **External Email - Please verify sender email address before responding.** Hi Neil and Mehmet, I hope you are doing well. I am emailing because I would like to invite you and your colleagues/students to participate in a new event I'm organizing at OU. The event is called "Hyperbolic Saturdays". Basically, I will have visitors come and lead a half-day discussion (usually on a Saturday) about a topic of their expertise. The topics are chosen in advance but the visitors are not supposed to prepare a seminar talk. I'm really hoping for a fruitful, lively exchange between the visitors and the participants. This event is funded by my NSF career grant. I can reimburse participants outside of OU for their travel (at full rate) and give a small per diem. Here's a website for the upcoming speakers: http://www.math.ou.edu/~jing/hyperbolic/<https://nam04.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.math.ou.…> The first hyperbolic Saturday will take place on August 24. The visitor is Kasra Rafi and the topic will be on basic hyperbolic geometry, particularly the action of SL(2,Z) on SL(2,R). The location will be somewhere in the math department but the room is TBD. I anticipate the schedule of the event to look as follows: 9:30-10 -- coffee 10-12-ish -- discussion (with break) lunch If you could pass the word to people in your department who might be interested, that would be great. Please tell them to contact me if they are interested. Thank you in advance. Have a great semester! Best, JIng

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Seminar this semester
by Hoffman, Neil 14 Aug '19

14 Aug '19

Hello everyone, This semester our seminar will be at the usual time 3:30 on Tuesdays and in the usual place MSCS 509. It will also be followed by the usual topology dinner 5:30 at Hideaway. Please plan office hours according if you have the flexibility. The only thing unusual is that we will be having a visitor in the first week and then the organizational meeting. See you there. Best, Neil ______________________ 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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Today in Topology
by Hoffman, Neil 07 May '19

07 May '19

Hello everyone, We have just one talk for the end of the semester. Hailey will be speaking to us today in MSCS 445 (the corner room) at 3:30. Her title and abstract are below: A hyperbolic structure on the $5_2$ knot complement Speaker: Hailey Bodiford, Oklahoma State University Date: May 7, 2019 Time: 3:30 PM Room: MSCS 445 Abstract: I will discuss a method for finding a hyperbolic structure on the 52 knot complement. ______________________ 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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Today in Topology
by Hoffman, Neil 23 Apr '19

23 Apr '19

Today we are happy to welcome Michelle Chu back. She is stopping by here before going off to redbud this weekend. Also, today after seminar we can organize redbud travel as best as possible. Title: Coxeter groups, arithmetic reflection groups, and Vinberg’s algorithm Speaker: Michelle Chu, UCSB Date: Apr 23, 2019 Time: 3:30 PM Room: MSCS 509 Abstract: Coxeter groups and arithmetic reflection groups are broad classes of groups relevant to the study of hyperbolic manifolds. To make this connection more concrete we can build a fundamental domain for a hyperbolic reflection group using Vinberg’s algorithm. In this expository talk I will introduce and discuss these ideas, which will serve to give some of the important background for my talk at Redbud later in the week. ______________________ 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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Birch today
by Hoffman, Neil 16 Apr '19

16 Apr '19

Hello everyone, Today we are very happy to have Birch speaking in seminar. His title and abstract are below. Also, we have two more talks this semester. Michelle Chu from UCSB next week and Hailey Bodiford in three weeks. Title: Prime Decomposition of Surfaces by Crushing Speaker: Birch Bryant, Oklahoma State University Date: Apr 16, 2019 Time: 3:30 PM Room: MSCS 5109 Abstract: Joint project with William Jaco. Following the steps for the prime decomposition of 3-manifolds laid out in the Jaco & Rubinstein paper “0- Efficient Triangulations of 3- Manifolds” we construct the analogous (and well known) result for surfaces. That being the torus and real projective plane are the prime surfaces with respect to the connect sum operation on surfaces. Further the decomposition of surfaces into prime elements can be written uniquely up to homeomorphism. ______________________ 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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Today in topology
by Hoffman, Neil 02 Apr '19

02 Apr '19

Today, I will be speaking in topology. Title: Restricting covers and symmetries of Dehn fillings Speaker: Neil Hoffman, Oklahoma State University Date: Apr 2, 2019 Time: 3:30 PM Room: MSCS 509 Abstract: This talk will focus on the thick/thin decomposition of hyperbolic 3-manifolds and 3-orbifolds. I will describe how it relates to joint work in progress with Millichap and Worden. ______________________ 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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Today in Seminar
by Hoffman, Neil 26 Mar '19

26 Mar '19

Hello everyone, Today Christian Millichap will be speaking in seminar. Robert is organizing a lunch today so meet at 12:30 outside his office if you are interested in that. Christian's title and abstract are given below. Title: Commensurability classes of fully augmented pretzel links Speaker: Christian Millichap, Furman University Date: Mar 26, 2019 Time: 3:30 PM Room: MSCS 509 Abstract: Fully augmented links (FALs) are a large class of links whose complements admit hyperbolic structures that can be explicitly described in terms of combinatorial information coming from their respective link diagrams. In this talk, we will examine an infinite subclass of FALs that are constructed by fully augmenting pretzel links and describe how to build their hyperbolic structures. We will then discuss how we can use the geometries of these link complements to analyze arithmetic properties and commensurability classes of these links. This is joint work with Jeffrey S. Meyer and Rolland Trapp. ______________________ 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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