[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 Louis-Hadrien Robert and Emmanuel Wagner. It benefits from logistical support from the CNRS and the university of Geneva.


25/02/2021
NO SEMINAR.

04/03/2021
  • Speaker: Daniel Ruberman (Brandeis University).
  • Title: A Levine–Tristram invariant for knotted tori.
  • Abstract: In 1969, Tristram and Levine independently introduced an integer-valued function of a knot, depending on the choice of a unit complex number. It gives rise to a concordance invariant that in turn shows that the the concordance group is infinitely generated. I will explain a generalization of this invariant to the setting where the 3-sphere is replaced by X, a homology 𝕊1×𝕊3, and the knot is replaced by an embedded torus (that carries the first homology). I will show how to compute this invariant, and discuss its relation to recent work of Echeverria that counts SU(2) connections on the complement of the torus with specified holonomy on the meridian.


11/03/2021
  • Speaker: Akram Alishahi (University of Georgia).
  • Title: TBA.
  • Abstract: TBA.


18/03/2021
  • Speaker: Ricard Riba Garcia (Universitat Autònoma de Barcelona).
  • Title: TBA.
  • Abstract: TBA.


25/03/2021

01/04/2021
  • Speaker: Maciej Borodzik (Uniwersytet Warszawski).
  • Title: Non-rational, non-cuspidal plane curves via Heegaard Floer homology.
  • Abstract: Let C be a complex curve in ℂℙ2. Using d-invariants from Heegaard Floer theory we provide topological constraints for possible singularities of C. The novelty is that we do not need to assume that C is rational, or that all its singularities have one branch, so we generalize previous results of Bodnar, Borodzik, Celoria, Golla, Hedden and Livingston. As an application, we show precise examples of surfaces in ℂℙ2, for which "genus cannot be traded for double points". This is a joint project with Beibei Liu and Ian Zemke.


08/04/2021
  • Speaker: Andrew Lobb (Durham University).
  • Title: Four-sided pegs fitting round holes fit all smooth holes.
  • Abstract: Given a smooth Jordan curve and a cyclic quadrilateral (a cyclic quadrilateral is a quadrilateral that can be inscribed in a circle) we show that there exist four points on the Jordan curve forming the vertices of a quadrilateral similar to the one given. The smoothness condition cannot be dropped (since not all cyclic quadrilaterals can be inscribed in all triangles). The proof involves some results in symplectic topology. No prior knowledge assumed. Joint work with Josh Greene.


15/04/2021, 22/04/2021
NO SEMINAR.

29/04/2021
  • Speaker: David Leturcq (Research Institute for Mathematical Sciences, Kyōto University).
  • Title: TBA.
  • Abstract: TBA.


06/05/2021
  • Speaker: Jacob Rasmussen (University of Cambridge)
  • Title: TBA.
  • Abstract: TBA.


13/05/2021

20/05/2021
  • Speaker: Delphine Moussard (Aix–Marseille Université)
  • Title: TBA.
  • Abstract: TBA.


27/05/2021
  • Speaker: Raphael Zentner (Universität Regensburg)
  • Title: TBA.
  • Abstract: TBA.


17/06/2021
  • Speaker: Vincent Colin (Université de Nantes)
  • Title: TBA.
  • Abstract: TBA.


24/06/2021

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