Click here for the notes of a talk that I gave, based on the results of this paper, on 7 September 2020 at (virtually) the Knots and representation theory seminar, Moscow.

Our (five) Reidemeister moves for 3-crossing diagrams are drawn on page 8 of these notes, and pages 9–12 contain a sketch proof of our main result — that they form a *complete* set of Reidemeister moves for 3-crossing diagrams.

The video of this talk is **here**.