Knot Theory Seminar

Welcome to the Groningen Knot Theory Seminar!

Roland van der Veen and Jorge Becerra are organising a weekly seminar on Knot Theory aimed at Master's students and 3rd year Bachelor's students. Participants are encouraged to give talks about the upcoming topics. If you would like to volunteer for a talk please let us know!

We meet on Thursdays 15:00 - 17:00. For more information about the seminar please see the course description below or contact Roland or Jorge.

Knot Theory is an active part of mathematics with many connections with topology, representation theory, quantum physics, etc. We plan to study the basics of this subject. Some basic knowledge on group theory, topological spaces and fundamental group will be useful but not strictly necessary.

Schedule

  • * Colloquium Mathematics *: 4 February 2020, room 5161.0293

16:00 - 17:00: Dror Bar-Natan (University of Toronto): Algebraic Knot Theory. See handout here.

  • 6 February 2020, room 5161.0289

15:00 - 15:30: Roland van der Veen: Overview.

15:45 - 16:15: Jorge Becerra: Review of the fundamental group. See here for more on free groups, etc.

16:30 - 17:00: Exercise hour.

  • 13 February 2020, room 5161.0289

15:00 - 15:45: Guest lecture by Dror Bar-Natan (University of Toronto): Finite type invariants (part 1). Watch here the video recording.

15:45 - 16:00: Break.

16:00 - 17:45: Dror Bar-Natan: Finite type invariants (part 2). Watch here the video recording.

Remark: In Spring 2014, Dror gave a course on finite type invariants in Toronto, watch here the video recordings.

  • 20 February 2020, room 5161.0267

15:00 - 15:30: Oscar Koster: Knots and links, equivalence of links, connected sum of knots, Reidemeister moves. Oscar's notes.

15:45 - 16:15: Exercise hour.

16:30 - 17:00: Jorge Becerra: First knot invariants: linking number, unknotting number, crossing number, 3-colorability.

  • 27 February 2020, room 5161.0162

15:00 - 15:30: Wout Moltmaker: The knot group, Wirtinger presentation and examples. Wout's slides and exercises.

15:30 - 17:00: No seminar.

  • 5 March 2020, room 5161.0289

15:00 - 15:30: Aarnout Los: Elementary ideals. Aarnout's notes.

15:45 - 16:15: Exercise hour.

16:30 - 17:00: Jorge Becerra: The Alexander polynomial: the algebraic way. Jorge's notes.

  • 12 March 2020, room 5161.0041b

15:00 - 15:30: Roland van der Veen: Computing knot groups and Alexander polynomials.

15:45 - 17:00: Extra-exercise hour. Problem sheet.


  • From Friday 13 March until at least September, all physical lectures, seminars, tutorials and exams at RuG will be cancelled, due to the coronavirus pandemic. For the time being we will resume the seminar in an online setting, where students can talk about their Bachelor's or Master's projects.


  • 21 May 2020, online meeting (join here from your RuG account)

15:00 - 16:00: Aarnout Los: Invariants on families of knot diagrams. Aarnout's notes.


  • 28 May 2020, online meeting (join here from your RuG account)

15:00 - 16:00: Jorge Becerra: The Alexander polynomial: the topological way. Jorge's slides.


  • 4 June 2020, online meeting (join here from your RuG account)

15:00 - 16:00: Jermain Walle: Hyperbolic knots. Jermain's slides.


  • 11 June 2020, online meeting (join here from your RuG account)

15:00 - 16:00: Oscar Koster: Vassiliev Invariants. Oscar's slides.


  • 18 June 2020, online meeting (join here from your RuG account)

15:00 - 16:00: Roland van der Veen: Computing Alexander with Mathematica. Roland's Mathematica notebook.


  • 25 June 2020, online meeting (join here from your RuG account)

15:00 - 16:00: Wout Moltmaker: Braided diagrams. Wout's slides.


  • 2 July 2020, no seminar!


  • 9 July 2020, online meeting (join here from your RuG account)

15:00 - 16:00: Jorge Becerra: Categorification, topology and knots. Jorge's notes.

Futher reading on categorification: this presentation (easier) and this paper (harder).

For more about the categorification of the Alexander polynomial, see this introduction to Heegaard-Floer homology.


  • 16 July 2020, online meeting (join here from your RuG account)

15:00 - 16:00: Guest talk by Jesse Fröhlich (University of Toronto): A tale of two Alexander's: Jana Calculus and the Multivariable Alexander polynomial.


  • 23 July 2020, online meeting (join here from your RuG account)

15:00 - 16:00: Roland van der Veen: OU-tangles. Roland's paper (joint with D. Bar-Natan and Z. Dancso).


  • Summer break.



Course description

Format

Participants are expected to give at least 2 talks of 30 min each, being strongly encouraged to make a handout. Every speaker will also bring a couple of exercises to discuss in the exercise slot. Participants are expected to attend every seminar meeting.

References

Knot Theory

  • Adams, C. - The Knot Book.

  • Chmutov, S. & Duzhin, S. & Mostovoy , J. - Introduction to Vassiliev Knot Invariants

  • Crowell, R.H. & Fox, R.H. - Introduction to Knot Theory.

  • Lickorish, W.B.R. - An introduction to Knot Theory.

  • Rolfsen, D. - Knots and Links

Algebraic Topology