Regular Seminar Fabian Ruhle (CERN)
[For zoom details please email s.nagyATqmul.ac.uk There will be a pre-seminar for students at 13:30] Knot theory plays an important role in physics, mathematics and biology. Characterizing knots is, however, a difficult task. There are different ways to represent a knot (e.g. via braids, Gauss codes, Dowker-Thistlethwaite notation), and many knot invariants exist (e.g. the Alexander polynomial, Jones polynomial, determinant, slice genus). However, it is not known whether these can be used to identify a trivial knot, the so-called unknot. We use different machine learning techniques to tackle this question. First, we use a very recent neural network architecture developed for natural language processing, called the reformer, to decide whether a given knot is the unknot. We also apply Reinforcement Learning to solve the harder problem of finding a set of Reidemeister/Markov moves that explicitly simplify a given knot as much as possible. If the algorithm finds a sequence of moves that removes all crossings of a knot in a given representation, then this knot is provably the unknot.