[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
21/10/2021
- 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.
28/10/2021
- 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.
4/11/2021Exceptionnally at 15:00 CET
- Speaker: Liam Watson (University of British Columbia )
- Title: TBA
11/11/2021
18/11/2021
25/11/2021NO SEMINAR
2/12/2021
9/12/2021
16/12/2021
