A computational arms race in knot theory: Algorithms vs examples

Alex He
Sydney

Abstract

This talk will begin with a selective survey of computation involving knots and 3-manifolds, with a bias towards techniques using normal surfaces. I will then present some recent developments in the "arms race" between designing effective algorithms versus constructing hard examples. On the algorithms side, I will mention a recent algorithm for recognising composite knots, developed jointly with Eric Sedgwick and Jonathan Spreer. On the side of hard examples, I will discuss ongoing work with Corentin Lunel on procedural generation of hard unknot diagrams and hard 3-sphere triangulations.