Machine Learning for Pure Math

Abstract: Progress in machine learning (ML) is poised to revolutionize a variety of STEM fields. But how could these techniques — which are often stochastic, error-prone, and blackbox — lead to progress in pure mathematics, which values rigor and understanding? I will exemplify how ML can be used to generate conjectures in a Calabi-Yau singularity problem that is relevant for physics, and will demonstrate how reinforcement learning can yield truth certificates that rigorously demonstrate properties of knots. The second half of the talk will utilize ML theory instead of applied ML. Specifically, I will develop a neural tangent kernel theory appropriate for flows in the space of metrics (realized as neural networks), and will realize Perelman’s formulation of Ricci flow as a specialization of the general theory.

machine learningMathematics

Audience: researchers in the discipline

Mathematics and Machine Learning

Series comments: Contact the Organizers to get the Zoom Coordinates.