### [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

**15/02/2024**
- Speaker: Alison Beth Miller (University of Michigan)
- Title:
**Disjoint Seifert surfaces and composition of binary quadratic forms**
- Abstract: Motivated by a recent construction of Hayden-Kim-Miller-Park-Sundberg exhibiting two Seifert surfaces for the same knot that are disjoint when pushed into the 4-ball, one can ask the
following question: given two Seifert matrices that are S-equivalent, when can we find a knot having two Seifert surfaces realizing each of these matrices?

I'll give some background on this question and then talk about joint work with Menny Aka, Peter Feller, and Andreas Wiseer, where we give a complete answer to this in the genus 1 case
under the additional assumption that the two Seifert surfaces must be disjoint. I'll explain the main ingredient in our proof, which is number-theoretic, giving a new approach to Gauss
composition and the Bhargava cube law, in a concrete down-to-earth manner.