Machine learning assisted exploration for affine Deligne-Lusztig varieties

Abstract: In this interdisciplinary study, we describe a procedure to assist and accelerate research in pure mathematics by using machine learning. We study affine Deligne-Lusztig varieties, certain geometric objects related to a number of mathematical questions, by carefully developing a number of machine learning models. This iterated pipeline yields well interpretable and highly accurate models, thus producing strongly supported mathematical conjectures. We explain how this method could have dramatically accelerated the research in the past. A completely new mathematical theorem, found by our ML-assisted method and proved using the classical mathematical tools of the field, concludes this study. This is joint work with Bin Dong, Pengfei Jin, Xuhua He and Qingchao Yu.

machine learningmathematical physicscommutative algebraalgebraic geometryalgebraic topologycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Machine Learning Seminar

Series comments: Online machine learning in pure mathematics seminar, typically held on Wednesday. This seminar takes place online via Zoom.

For recordings of past talks and copies of the speaker's slides, please visit the seminar homepage at: kasprzyk.work/seminars/ml.html