Highly twisted knot diagrams

One easy way of representing knot is via a knot diagram. However, inferring properties of the knot from its diagram and deciding when two diagrams represent the same knot are quite difficult problems. Surprisingly, when the diagram is sufficiently “twisty“ then some structure starts to emerge. I will discuss two results of this nature: hyperbolicity of highly twisted knot diagrams and uniqueness of highly twisted plat diagrams.

Based on joint works with Yoav Moriah, Tali Pinsky and Jessica Purcell. All relevant notions will be explained in the talk.