Machine Learning Detects Terminal Singularities in Q-Fano Varieties

Explore the intersection of machine learning and algebraic geometry in this 48-minute talk from the Applied Algebraic Topology Network. Delve into the application of neural networks to study Q-Fano varieties, key components in the Minimal Model Program. Learn how a high-accuracy machine learning model was developed to detect terminal singularities in toric Fano varieties, leading to two significant outcomes: the formulation of a new combinatorial criterion for determining terminal singularities in Picard rank two toric varieties, and the first glimpse into the landscape of eight-dimensional Q-Fano varieties. Gain insights into this collaborative research effort that bridges advanced mathematics and cutting-edge machine learning techniques.