Tancredi Gherardini (Queen Mary’s College, London) will speak in the geometry seminar on 4th April, at 2pm in the Salle des Profs (9th floor of building NO). Tancredi’s title is “AInstein: Numerical Einstein Metrics through Machine Learning” and his abstract is below.
In this talk, we will discuss a very recent numerical scheme based on semi-supervised machine learning, “AInstein”, which approximates generic Riemannian Einstein metrics on a specified manifold (arXiv:2502.13043). We will begin by reviewing the first applications of machine learning to find numerical Calabi-Yau metrics, and then present our generalisation of those approaches. We will summarise the results obtained with AInstein so far, which concern Einstein metrics on spheres of various dimensions. A long-standing open question in this context is the existence of Ricci-flat metrics on S^4 and S^5, for which our results provide heuristic numerical evidence against. Finally, we will comment on the numerous possible extensions and further applications of AInstein.