Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curves

Abstract: We introduce in the context of Calabi-Yau manifolds, and then apply machine-learning to, the study of dessins d'enfants. Specifically, we investigate a class of dessins which reside at the intersection of the investigations of modular subgroups and extremal elliptic K3 surfaces. A deep feed-forward neural network performs classification of Galois extension degree over the rationals, known to be a difficult problem. The classifications reached accuracy 0.92 relatively quickly. In relation to papers: 2004.05218 & 2001.01212

Mathematics

Audience: researchers in the topic

Seminario de Geometría y Física - Matemática UCN-USP