Generating Calabi–Yau Manifolds with Machine Learning

Abstract: Calabi–Yau n-folds can be obtained as hypersurfaces in toric varieties built from (n+1)-dimensional reflexive polytopes. Calabi–Yau 3-folds are of particular interest in string theory as they reduce 10-dimensional superstring theory to 4-dimensional quantum field theories with N=1 supersymmetry. We generate Calabi–Yau 3-folds by generating 4-dimensional reflexive polytopes and their triangulations using genetic algorithms and reinforcement learning respectively. We show how, by modifying the fitness function of the genetic algorithm, one can generate Calabi–Yau manifolds with specific properties that give rise to certain string models of particular interest.

machine learningmathematical physicscommutative algebraalgebraic geometryalgebraic topologycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Machine Learning Seminar

Series comments: Online machine learning in pure mathematics seminar, typically held on Wednesday. This seminar takes place online via Zoom.

For recordings of past talks and copies of the speaker's slides, please visit the seminar homepage at: kasprzyk.work/seminars/ml.html