[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


20/01/2022
  • Speaker: Filip Misev (Universität Regensburg)
  • Title: Families of fibred knots with the same Seifert form
  • Abstract: We will construct an infinite family of fibred, quasipositive knots having all the same Seifert matrix. The knots can be distinguished by the dilatation of their geometric monodromy. I will explain what these properties mean and why such families of knots might be of interest for the study of knot concordance.


27/01/2022
  • Speaker: Olga Plamenevskaya (Stony Brook University)
  • Title: Unexpected Stein fillings, rational surface singularities, and line arrangements
  • Abstract: A link of an isolated complex surface singularity is a 3-manifold obtained by intersecting the surface with a small sphere centered at the singular point. The link carries a canonical contact structure, given by the complex tangencies. Milnor fibers of possible smoothings of the singular point give Stein fillings for this contact structure; deformations of the singularity give rise to Stein cobordisms between the corresponding links. This leads to many interesting questions regarding the interplay of algebraic geometry, topology, and symplectic geometry.
    After setting the stage, we will focus on the following question: do Milnor fibers and the resolution of a surface singularity yield ALL possible Stein fillings of its link? This is known to hold in some simple cases, eg for lens spaces. We show that even in the "next simplest" case, for many rational singularities, there is a plethora of "unexpected" Stein fillings that do not arise from Milnor fibers of any smoothings. To compare fillings and smoothings, we use T.de Jong-D.van Straten's description of Milnor fibers of certain rational surface singularities in terms of deformations of associated singular plane curves. On the symplectic side, we develop an analogous description of the Stein fillings via certain more general arrangements of curves. "Unexpected" arrangements then give rise to "unexpected" fillings. (Joint work with L. Starkston.)
    All the discussion will be from the topological perspective, with minimal input from algebraic geometry.


03/02/2022
  • Speaker: Paul Wedrich (Universität Hamburg)
  • Title: A skein relation for singular Soergel bimodules
  • Abstract: Soergel bimodules categorify Hecke algebras and lead to invariants of braids that take values in monoidal triangulated categories. In this process, the quadratic `skein relation' on Artin generators is promoted to a distinguished triangle. I will talk about an analog of this relation in the setting of singular Soergel bimodules and Rickard complexes, in which the distinguished triangle gets replaced by a longer one-sided twisted complex. Joint work with M. Hogancamp and D.E.V. Rose.


10/02/2022
  • Speaker: Linh Truong (University of Michigan)
  • Title: TBA
  • Abstract: TBA


17/02/2022
  • Speaker: Paula Truöl (ETH Zürch)
  • Title: TBA
  • Abstract: TBA


24/02/2022
  • Speaker: Oliver Singh(Durham University)
  • Title: TBA
  • Abstract: TBA


03/03/2022
  • Speaker: Paolo Ghiggini (Université de Nantes)
  • Title: TBA
  • Abstract: TBA


10/03/2022
  • Speaker: TBA
  • Title: TBA
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17/03/2022
  • Speaker: TBA
  • Title: TBA
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24/03/2022
  • Speaker: Thang T. Q. Le (Georgia Institute of Technology)
  • Title: TBA
  • Abstract: TBA


31/03/2022
  • Speaker: TBA
  • Title: TBA
  • Abstract: TBA


07/04/2022
  • Speaker: TBA
  • Title: TBA
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14/04/2022
NO SEMINAR.


21/04/2022
  • Speaker: TBA
  • Title: TBA
  • Abstract: TBA


28/04/2022
  • Speaker: TBA
  • Title: TBA
  • Abstract: TBA


30/06/2022
  • Speaker: Vincent Florens (Université de Pau et des Pays de l'Adour)
  • Title: TBA
  • Abstract: TBA

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