Calabi-Yau metrics, machine learning, and the spectrum of the Laplace operator
Overview
Calabi-Yau manifolds have played a role in advances in both mathematics and physics, and are particularly important for deriving realistic models of particle physics from string theory. Unfortunately, very little is known about the explicit metrics on these spaces, other than for tori, leaving us unable to compute particle masses or couplings in these models. In this talk I will discuss the numerical methods available for computing these metrics and review recent progress on using machine learning to find these metrics. Using this numerical 'data' of the metric, I will compute the spectrum of the Laplace operator acting on (p,q)-forms, taking a crucial step towards computing masses and couplings in physically relevant theories.
