Approximating Hermitian Yang--Mills connections on vector bundles

Justin Tan

Keywords: physics, differential geometry, geometric machine learning, equivariance

TL;DR: Solve nonlinear PDEs on manifolds by parameterising tensor fields of interest to physicists in a fully equivariant way.

Abstract: Geometric objects of interest to physicists typically arise as the solution to challenging nonlinear systems of PDEs on manifolds. In this work, we propose a simple two--stage procedure to approximate one such system, the Hermitian Yang--Mills equations on a holomorphic vector bundle over a K\"ahler manifold. The main challenge here is developing an appropriate fully--differentiable parameterisation of the associated tensor fields in a manner which respects the symmetries and topology of the manifold.

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Submission Number: 63