New Calabi–Yau manifolds from genetic algorithms

From [Formula: see text]-dimensional reflexive polytopes one can construct [Formula: see text] complex-dimensional Calabi–Yau manifolds as hypersurfaces in toric varieties. In this contribution to the DANGER 3: Data Numbers and Geometry conference proceedings, we summarise previous work [P. Berglund, Y.-H. He, E. Heyes, E. Hirst, V. Jejjala and A. Lukas, New Calabi–Yau Manifolds from Genetic Algorithms (2023)] generating reflexive polytopes using genetic algorithms. As a proof of principle, we demonstrate that the genetic algorithm can reproduce known reflexive polytopes in two, three and four dimensions. Motivated by this result, we construct five-dimensional reflexive polytopes and establish that many of these are not in existing datasets and therefore give rise to new Calabi–Yau four-folds.