Daniel Tubbenhauer - How good are (quantum) knot invariants?

He diligently posts at least two short talks on his YouTube channel every Saturday, and occasionally he re-enacts lectures he has given to a real audience, rather than a virtual audience on YouTube. This is one such re-enacted lecture on the Poincaré conjecture, Quantum Knot Invariants and the Jones Polynomial.  It's really excellent. Knot theory is now very clearly a part of polymer chemistry, and, when you think about that, it's really a very interesting thing. It means that the properties of organic chemical compounds like long-chain polymers are simply not reducible to the properties of their constituent atoms. Full stop!

See the paper Big data comparison of quantum invariants by Daniel Tubbenhauer and Victor Zhang and the online database Knot Invariant Comparison by Zhang. Also (54:17) the Dioscuri Center in Topological Data Analysis site https://dioscuri-tda.org/BallMapperKnots.html. These data are only up to about 15 crossings. So how much do we know now about long chain polymer chemistry?

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ICM 2018 Talk Knots, 3-Manifolds and Instantons by Kronheimer and Mrowka


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