Davide Michieletto (University of Edinburgh): Topologically active polymers and AI-guided discovery of knot invariants

In this talk I will give an overview of the research in my group focusing on two major themes: “topologically active polymers” and “AI-guided discovery of knot invariants”.

Topologically active polymers:
Polymer physics successfully describes most of the polymeric materials that we encounter everyday. Despite this, it heavily relies on the assumption that polymers do not change topology (or architecture) in time or that, if they do alter their morphology, they do so in equilibrium. This assumption spectacularly fails for DNA in vivo, which is constantly topologically re-arranged by ATP-consuming proteins within the cell nucleus.
I will present some work inspired by this phenomenal feat, where we study entangled DNA which can selectively alter their topology and architecture in time and may expend energy to do so.

AI-guided discovery of knot invariants:
We have recently demonstrated that Neural Networks (NN) can learn to identify and classify complex knotted curves up to 10 crossings with high accuracy. Even more strikingly, NNs can be trained to distinguish so-called “mutant” knots, such as Conway and Kinoshita-Terasaka knots, that share many topological invariants. This impressive feat is achieved when NNs are trained using a “segment-to-segment” writhe, a quantity that measures the level of entanglement between segments along the knotted molecule or polymer. Our results suggest that understanding how NNs classify knots could potentially guide mathematicians in formulating new topological invariants in knot theory.

Zoom Information:

https://us02web.zoom.us/j/2022111100

(Meeting code: 2022111100 Password: skcm2)