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

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

        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.

        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.

        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. 

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

        15:30 - 17:00:  No seminar.

        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.

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

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



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


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


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


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


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


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



        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.


        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.


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




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

Algebraic Topology