AI for Math: From Group Theory to Discrete Holography

par Fedor Levkovich-Maslyuk (City University, London)

lundi 14 sept. 2026, 14:00 → 15:30 Europe/Paris

Centre de conférences Marilyn et James Simons (IHES)

I will describe how one can use modern machine learning methods to attack open problems in group theory. I will show how ideas from AI, pure math, integrability, string theory and quantum information meet here in a highly productive way. I will focus on much-studied Cayley graphs of permutation groups, which are often very hard to explore due to their enormous size. I will describe how a modern ML approach overcomes this challenge and provides efficient pathfinding on these huge graphs. The outcome is a large set of new results and conjectures that in particular sharpen famous bounds on the diameters of these graphs. These results also hint at the existence of a novel, discrete string-like duality for this setting. It provides a realisation of the paradigm "complexity = volume" from AdS/CFT holography, and may potentially be applicable to a wider range of AI tasks. Lastly I will outline some new results for combinatorics of quantum periods and how this could help in improving these ML approaches. Based on arXiv:2509.19162, 2603.22195 and work to appear. Our code is publicly available as the CayleyPy library.

 

 

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