Seminar series
Date
Wed, 29 Oct 2025
16:00
16:00
Location
L6
Speaker
Sam Ketchell
Organisation
Mathematical Institute University of Oxford
Abstract: There exist diagrams of the unknot that are "hard" in the sense that any sequence of Reidemeister moves rearranging them into the standard unknot diagram must at some point increase the crossing number beyond what it was originally. I will discuss how such diagrams can be produced and what is known and unknown about them.
Then, I will define and discuss the arc index of a knot, an invariant that behaves more nicely than the crossing number from this perspective, and in some other ways.