Mdtop

mdtop@mathdept.okstate.edu

247 discussions

Today in topology
by Hoffman, Neil 18 Nov '20

18 Nov '20

Hello everyone, Today we are really happy to have Maria Trnkova dropping by (virtually) to give a talk. Maria last spoke here at Redbud, so it's always nice to see a familiar face. Her title and abstract are below: Speaker: Maria Trnkova, UC Davis Date: Nov 18, 2020 Time: 3:45 PM Room: https://meet.google.com/frv-bgow-byi Abstract: A computer program ”SnapPea” and its descendant “SnapPy” compute many invariants of a hyperbolic 3-manifold M. Some of their results can be rigorous but some not. In this talk we will discuss computation of geodesics length and will mention a number of applications when it is crucial to know the precise length spectrum up to some cut off. C.Hodgson and J.Weeks introduced a practical length spectrum algorithm implemented in SnapPea. The algorithm uses a tiling of the universal cover by translations of a Dirichlet domain of M by elements of a fundamental group. In theory the algorithm is rigorous but in practice its output does not guarantee the correct result. It requires to use the exact data for the Dirichlet domain which is available only in some special cases. We show that under some assumptions on M an approximate Dirichlet domain can work equally well as the exact Dirichlet domain. Our result explains the empirical fact that the program ”SnapPea” works surprisingly well despite it not using exact data. ______________________ 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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Topology seminar, Wednesday 3:45pm
by Henry Segerman 10 Nov '20

10 Nov '20

Hi all, This week's speaker is Anna Parlak from the University of Warwick. Title: The taut polynomial and the Alexander polynomial Speaker: Anna Parlak, University of Warwick Time: Wednesday, November 11, 2020 - 3:45pm to 4:45pm Room: Virtual meeting https://meet.google.com/yyt-utuu-imr (note that this is a new link) Abstract: Landry, Minsky and Taylor recently introduced two polynomial invariants of veering triangulations – the taut polynomial and the veering polynomial. I will give the definition of the taut polynomial of a veering triangulation and explain its relationship with the Alexander polynomial of the underlying 3-manifold. I will also discuss how to interpret these results in the case when a veering triangulation carries a fibration over the circle. Thanks, Henry

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Redbud today at 9am
by Hoffman, Neil 08 Nov '20

08 Nov '20

Hello everyone, Just a reminder that the virtual Redbud topology conference is happening today. https://redbud.math.ou.edu/fall-2020/schedule.html https://oklahoma.zoom.us/j/91847314850?pwd=NlhOYXBwWEEzTVBWOWZBckhjUVZFQT09 Meeting ID: 918 4731 4850 Passcode: C7DMd7VL The conference webpage has a gather town link to facilitate the kinds of conversations which could occur if we were in person. Here is the schedule: 9:00 − 9:45 Neil Hoffman Conjectures related to knot complement commensurability<https://redbud.math.ou.edu/fall-2020/schedule.html#Hoffman> 10:00 − 10:45 Nick Castro Isotopy classes of relatively trisected 4-manifolds with boundary<https://redbud.math.ou.edu/fall-2020/schedule.html#Castro> 11:00 − 11:45 Derrick Wigglesworth The Farrell-Jones Conjecture for (most) hyperbolic-by-cyclic groups<https://redbud.math.ou.edu/fall-2020/schedule.html#Wigglesworth> lunch break 1:30 − 2:15 Hitesh Gakhar Künneth formulae in persistent homology<https://redbud.math.ou.edu/fall-2020/schedule.html#Gakhar> 2:30 − 3:15 Wenwen Li Multi-persistent homology of restricted configuration spaces of metric graphs<https://redbud.math.ou.edu/fall-2020/schedule.html#Li> 3:30 − 4:15 Henry Segerman Raytracing and raymarching simulations of non-euclidean geometries<https://redbud.math.ou.edu/fall-2020/schedule.html#Segerman> 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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Tomorrow in Topology Seminar
by Hoffman, Neil 03 Nov '20

03 Nov '20

Hello everyone, Tomorrow we have Sam Ballas speaking in topology seminar. His title and abstract are below. Title: Gluing equations in low dimensional geometry Speaker: Sam Ballas, Florida State University Date: Nov 4, 2020 Time: 3:45 PM Central (4:45 PM Eastern) Room: google meet link: https://meet.google.com/frv-bgow-byi Abstract: Geometric structures are ubiquitous objects in low dimensional topology. Roughly speaking, such structures allow one to transport geometry from some nice model space onto a manifold by using charts with appropriate transition functions. Common examples include familiar objects such as Euclidean and hyperbolic structures as well as more exotic structures like affine and Anti-de Sitter structures. Despite their importance, in practice it can be hard to construct examples because the space of all possible charts is very large. In this context, the goal of this talk is to explain the philosophy that gluing equations can be viewed as a growing class of tools designed to “discretize” the problem of constructing geometric structures by using the combinatorial data of a triangulation to shrink the set of possible charts to a more manageable space (i.e. finite dimensional). This philosophy will be motivated by examples including Thurston’s original gluing equations for hyperbolic structures and more recent gluing equations of myself and Casella for projective structures. This work is joint with Alex Casella. ______________________ 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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Fall Redbud
by Hoffman, Neil 28 Oct '20

28 Oct '20

Hello everyone, Because of the ice storm the fall 2020 redbud conference will be on November 8th (originally it was going to be held this weekend). If you want to attend, you can find the registration form on the conference webpage: https://redbud.math.ou.edu/fall-2020/ ______________________ 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] This week in Topology
by Hoffman, Neil 28 Oct '20

28 Oct '20

Thanks to everyone who got back to me. It looks like we will have critical mass for seminar. See everyone at 3:45. Sent from my iPhone On Oct 28, 2020, at 11:36 AM, William Jaco <jaco(a)math.okstate.edu> wrote: Right now all is good. I can be on. William H. "Bus" Jaco Regents Professor, Grayce B. Kerr Chair Department of Mathematics On Tue, Oct 27, 2020 at 9:37 PM Hoffman, Neil <nhoffman(a)math.okstate.edu<mailto:nhoffman@math.okstate.edu>> wrote: Hello everyone, Sorry for the two emails. First, I hope everyone is okay. With campus closed tomorrow and internet down around Stillwater, I wanted to check in to see if people still could make seminar tomorrow. If we can get a good enough turnout, I am inclined to try to hold seminar tomorrow. If possible, could you send an email back that you can make seminar tomorrow if it’s held? I might have to assume that those that don’t respond are without internet, but if you are getting this on your phone because your home internet is down that would be helpful for me to know. Best, Neil ___________________ Neil Hoffman On Oct 27, 2020, at 3:31 PM, Hoffman, Neil <neil.r.hoffman(a)okstate.edu<mailto:neil.r.hoffman@okstate.edu>> wrote: Hello everyone, This week we are really excited to have Roman Aranda (virtually) coming down from Iowa to speak. His title and abstract are below: 4-manifolds with small trisection genus Speaker: Roman Aranda, University of Iowa Time: Oct 28, 2020, 3:45 PM Room: Virtual meeting https://meet.google.com/frv-bgow-byi<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fmeet.goog…> Abstract: In 2016, D. Gay and R. Kirby proved that every closed 4-manifold can be decomposed as the union of three 4-dimensional simple pieces with triple intersection a closed orientable surface of genus g. This decomposition is called a trisection of genus g for M. In 2018, M. Chu and S. Tillmann gave a lower bound for the trisection genus of a closed 4-manifold in terms of the rank of its fundamental group. In this talk, we show that given a group G, there exists a 4-manifold M with fundamental group G with trisection genus achieving Chu-Tillmann’s lower bound. The proof uses techniques of knot theory in simple 3-manifolds. ___________________ Neil Hoffman _______________________________________________ Mdtop mailing list Mdtop(a)mathdept.okstate.edu<mailto:Mdtop@mathdept.okstate.edu> http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/mdtop<https://nam04.safelinks.protection.outlook.com/?url=http%3A%2F%2Fcauchy.mat…>

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This week in Topology
by Hoffman, Neil 27 Oct '20

27 Oct '20

Hello everyone, This week we are really excited to have Roman Aranda (virtually) coming down from Iowa to speak. His title and abstract are below: 4-manifolds with small trisection genus Speaker: Roman Aranda, University of Iowa Time: Oct 28, 2020, 3:45 PM Room: Virtual meeting https://meet.google.com/frv-bgow-byi Abstract: In 2016, D. Gay and R. Kirby proved that every closed 4-manifold can be decomposed as the union of three 4-dimensional simple pieces with triple intersection a closed orientable surface of genus g. This decomposition is called a trisection of genus g for M. In 2018, M. Chu and S. Tillmann gave a lower bound for the trisection genus of a closed 4-manifold in terms of the rank of its fundamental group. In this talk, we show that given a group G, there exists a 4-manifold M with fundamental group G with trisection genus achieving Chu-Tillmann’s lower bound. The proof uses techniques of knot theory in simple 3-manifolds. ___________________ Neil Hoffman

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This week in Topology
by Hoffman, Neil 20 Oct '20

20 Oct '20

This week we have Kate Petersen speaking. Her title and abstract are below. Title: Symmetries and surface detection for SL(2, C) character varieties of 3-manifolds Speaker: Kathleen Petersen, Florida State University Date: Oct 21, 2020 Time: 3:45 PM Room: https://meet.google.com/frv-bgow-byi Abstract: Culler, Morgan, and Shalen pioneered the detection essential surfaces in 3- manifolds through SL(2, C) character varieties. I’ll review these character varieties and detection, then discuss how symmetries of the 3-manifold affect this detection before concluding with some examples. This is joint work with Jay Leach. ______________________ 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 seminar
by Hoffman, Neil 14 Oct '20

14 Oct '20

Hello everyone, Today Ken Baker is coming by (virtually of course). His title and abstract are below. Title: The Morse-Novikov number of knots: connected sums and cabling Speaker: Ken Baker, University of Miami Date: Oct 14, 2020 Time: 3:45 PM Room: Virtual meeting: https://meet.google.com/frv-bgow-byi<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fmeet.goog…> Abstract: We show the Morse-Novikov number of knots in S 3 is additive under connected sum and unchanged by cabling, answering a question of M. Boileau and C. Weber as communicated by A. Pajitnov. ______________________ 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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Tomorrow in topology seminar
by Hoffman, Neil 06 Oct '20

06 Oct '20

Hello everyone, Tomorrow we have Achinta speaking in seminar. The link will be: https://meet.google.com/frv-bgow-byi His title and info can be found here: Title: Some results on the local topology of algebraic sets Speaker: Achinta Nandi, Oklahoma State University Date: Oct 7, 2020 Time: 3:45 PM Room: https://meet.google.com/frv-bgow-byi [https://www.gstatic.com/images/branding/product/2x/meet_96dp.png]<https://meet.google.com/frv-bgow-byi> Meet<https://meet.google.com/frv-bgow-byi> Real-time meetings by Google. Using your browser, share your video, desktop, and presentations with teammates and customers. meet.google.com Abstract: The topology of an algebraic set near a singular point is of fundamental interest in the study of analytic varieties. In this talk, we shall investigate the local topology of an algebraic set. After a brief description of the basics, we will prove some general facts about algebraic sets and establish results about the local topology of an algebraic set near regular points. A fundamental lemma concerning the existence of real analytic curves on the real algebraic sets will be proved to conclude the talk. Time permitting, we shall discuss some applications of the said lemma, in particular, a fibration theorem which is useful in describing the local topology near singular points. The talk is based on John Milnor’s ”Singular points of complex hypersurfaces”. ______________________ 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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