[K-OS] Knot Online Seminar

[K-OS] is an online research seminar which focuses on knot theory and low-dimensional topology. It happens every Thursdays from 14:00 to 15:00 (CET/CEST Berlin, Brussels, Madrid, Paris, Rome, Vienna, Warsaw, Zurich) on Zoom.

It is organized by Alexandra Kjuchukova, Lukas Lewark, Louis-Hadrien Robert and Emmanuel Wagner. It benefits from logistical support from the CNRS, the university of Paris and the university of Regensburg.

Forthcoming Talks

  • Speaker: Dror Bar-Natan (University of Toronto)
  • Title: Yarn-ball knots — A modest light conversation on how knots should be measured
  • Abstract: Let there be scones! Our view of knot theory is biased in favour of pancakes. Technically, if K is a 3D knot that fits in volume V (assuming fixed-width yarn), then its projection to 2D will have about V4/3 crossings. You'd expect genuinely 3D quantities associated with K to be computable straight from a 3D presentation of K. Yet we can hardly ever circumvent this V4/3>>V "projection fee". Exceptions include linking numbers (as we shall prove), possibly include the hyperbolic volume, and likely include finite type invariants (as we shall discuss in detail). But knot polynomials and knot homologies seem to always pay the fee. Can we exempt them? Joint with Itai Bar-Natan, Iva Halacheva, and Nancy Scherich. All the material for this talk, including up-to-date title and abstract, is available here.
  • Handout.

  • Speaker: Paolo Bellingeri (Université de Caen)
  • Title: Virtual Artin groups
  • Abstract: Virtual braid groups were introduced as a braid counterpart of virtual knots. From the combinatorial point of view it is interesting to remark that the virtual braid group VBn admits two surjective homomorphisms onto the symmetric group Sn. The kernels of these two homomorphisms have different meanings and applications: the first one, the virtual pure braid group VPn, coincides with the quasitriangular group QTrn considered by L Bartholdi, B Enriquez, P Etingof, E Rains in relation with Yang–Baxter equations, while the second one, usually denoted KBn, is an Artin group and it turns out to be a powerful tool to study combinatorial properties of VBn.
    Starting from the observation that the standard presentation of a virtual braid group mixes the presentations of the corresponding braid group Bn and of the corresponding symmetric group Sn together with the action of the symmetric group on its root system, we define for any Coxeter graph Γ a virtual Artin group VA[Γ] with a presentation that mixes the standard presentations of the Artin group A[Γ] and of the Coxeter group W[Γ] together with the action of W[Γ] on its root system. As in the case of VBn, we will define two surjective homomorphisms from VA[Γ] to W[Γ]: we will provide group presentations for these kernels (completely determined by root systems) and we will show several and general results on virtual Artin groups.
    This is a joint work with Luis Paris and Anne-Laure Thiel.

Exceptionnally at 15:00 CET
  • Speaker: Liam Watson (University of British Columbia )
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