SPS JC: de Sitter and Machine Learning

The problem of constructing de Sitter vacua in quantum theories of gravity is constrained by no-go theorems and made computationally challenging by the absence of supersymmetry. A popular approach to make it more tractableis to start from a supersymmetric compactification, such as on a Calabi-Yau manifold. This simplification comes at the price of greatly restricting the allowed physical sources and possible geometries.

In this introduction, I will discuss some of my works on how to break supersymmetry at the compactification scale by directly solving the equations of motion. This allows for more general internal geometries and thus more general physical configurations, including four-dimensional de Sitter vacua supported by Casimir energy on negatively-curved manifolds, and scale-separated AdS4 vacua.

However, describing the corresponding geometries in detail can sometimes require to solve Einstein-like PDEs on non-trivial manifolds. This problem is intractable even numerically, with standard methods. Luckily, Machine Learning is emerging as a method to overcome these difficulties, and we will discuss a recent proposal for using Machine Learning techniques to explicitly construct negatively-curved geometries.

Time permitting, we will also describe the other way around: how we can use insights from physics to design algorithms with broad applicability to Machine Learning and beyond, focusing on optimization and sampling algorithms obtained from energy-preserving chaotic Hamiltonians with non-standard kinetic terms.