Room P3.10, Mathematics Building — Online

Damián Mayorga Pena

Damián Mayorga Pena, Instituto Superior Técnico, Universidade de Lisboa
Machine learning Calabi-Yau metrics

Ricci flat metrics for Calabi-Yau threefolds are not known analytically. In this talk, I will discuss techniques from machine learning to deduce numerical flat metrics on Calabi-Yau two- and three-folds. In particular, I will focus on a particular type of approximation known as spectral neural networks. This type of network produces an exact Kähler metric. I will discuss the metric approximation for various examples, with particular focus on the Cefalú family of quartic two-folds, for which we study the corresponding characteristic forms. Furthermore, from the computation of the Euler characteristic, I will demonstrate that the numerical computations match the expectations, even in the case of singular geometries.