Enhancing Research in Algebraic Geometry with Artificial Intelligence

Algebraic geometry studies the solutions of systems of polynomial equations and the geometry of the spaces they form, called algebraic varieties. It is a classical subject, yet many of its central questions remain open.

This project aims to make progress on some of these questions with the help of artificial intelligence. We focus on problems that can be translated into combinatorics (cones, polytopes, configurations of curves, lattices) and are therefore well suited to computer assisted research. On top of this translation we train machine learning models, and then use Explainable AI techniques to extract human understandable information from them: conjectures, new invariants or counterexamples.