Machine Learning for Hilbert Series

TL;DR

This paper reviews the application of machine learning techniques to analyze and predict properties of Hilbert series, a fundamental concept in algebraic geometry with emerging relevance in theoretical physics.

Contribution

It provides a comprehensive overview of how machine learning is used to study Hilbert series, highlighting recent advances and potential future directions.

Findings

Machine learning models can predict Hilbert series properties accurately.

Data-driven approaches reveal new patterns in algebraic geometry.

Potential applications in theoretical physics are identified.

Abstract

Hilbert series are a standard tool in algebraic geometry, and more recently are finding many uses in theoretical physics. This summary reviews work applying machine learning to databases of them; and was prepared for the proceedings of the Nankai Symposium on Mathematical Dialogues, 2021.