DeepMind Workshop

Knot Theory and Machine Learning

Andras Juhasz, University of Oxford

The signature of a knot K in the 3-sphere is a classical  invariant that gives a lower bound on the genera of compact oriented surfaces in the 4-ball with boundary K. We say that K is hyperbolic if its complement admits a complete, finite volume hyperbolic metric. I will explain how we have used methods from machine learning to find an unexpected relationship between the signature and the cusp shape of a hyperbolic knot. This is joint work with Alex Davies, Marc Lackenby, and Nenad Tomasev.