[K-OS] Knot Online Seminar

[K-OS] is an online research seminar which focuses on knot theory and low-dimensional topology. Talks will be delivered by authors of recent arXiv articles that made a breakthrough in our field. It happens the 3rd Thursday of months from 16:15 to 17:15 (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 and the university of Paris.

If there is a recent arXiv preprint which you would like to see featured on the seminar, please email the organizers with your suggestion.

Forthcoming Talks

16/11/2023

• Speaker: Ivan Dynnikov (Steklov Mathematical Institute)
• Title: An algorithm for comparing Legendrian links (2309.05087)
• Abstract: The talk is based on my joint works with Maxim Prasolov and Vladimir Shastin, where we studied the relation between rectangular diagrams of links and Legendrian links. This relation allows for a complete classification of exchange classes of rectangular diagrams in terms of equivalence classes of Legendrian links and their symmetry groups. Since all rectangular diagrams of given complexity can be searched, this yields a method to algorithmically compare Legendrian links. Of course, the general algorithm has too high complexity for a practical implementation, but in some situations, the most time-consuming parts can be bypassed, which allows us to confirm the non-equivalence of Legendrian knots in several previously unresolved cases.

14/12/2023

• Speaker: Effie Kalfagianni (Michigan State University)
• Title: Jones diameter and crossing numbers of satellite knots
• Abstract: It has been long known that the quadratic term in the degree of the colored Jones polynomial of knot provides a lower bound of the crossing number the knot.
  I’ll discuss work, some joint with Christine Lee (2021) and some joint with Rob McConkey (2023), where we determine the class of knots for which this bound is sharp and give applications to computing crossing numbers of satellite knots.