Speaker: Dr. Salm Willem Adriaan (Université Libre de Bruxelles)

Title: Search for Z/2-eigenfunctions on the sphere using machine learning

Time: 10:30-11:30  June 9, 2026 (Tuesday)

Place: MCM110

Abstract: Z/2-eigenfunctions of the Laplacian on the 2-sphere play an important role in geometric analysis, appearing in the blow-up analysis of multivalued harmonic functions. These objects arise naturally in gauge theory, where they model diverging sequences of solutions to equations such as the Generalized Seiberg–Witten equations.

The goal of this talk is to introduce a pure mathematician into the world of machine learning. We ask whether machine learning can be used to find examples of these Z/2-eigenfunctions. We will introduce the basics of neural networks and deep learning and explain how these tools can be used to numerically solve PDEs on manifolds. We describe how we created an AI that recovered the non-constructive examples of Taubes–Wu and Chen–He. Along the way, we discuss the practical challenges that arise when applying machine learning techniques to problems in geometric analysis.