Mathematics Colloquium

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Is the Jones representation faithful?

Speaker: Geordie Williamson, University of Sydney

Location: Warren Weaver Hall 1302

Date: Monday, October 27, 2025, 3:45 p.m.

Synopsis:

Can we tell if a knot is an unknot? I’ll discuss the “Jones unknot problem”, which is the tantalising conjecture that would give a simple answer to this problem. I’ll then discuss the relation to the faithfulness of certain group representations, which have occupied lots of (human) neural networks for over forty years. Then I’ll outline a program to use (artificial) neural networks to attack the same problem. So far, we haven’t been able to resolve this question. However, our adventures suggest an interesting use of neural networks to attack hard search problems, which may be useful elsewhere. This is based on joint work with Charton, Gibson, Narayanan and Yacobi.