Higgs bundles without geometry

TL;DR

This paper provides an informal overview of the linear algebra underlying the moduli space of Higgs bundles, highlighting their mathematical structure without relying on geometric details.

Contribution

It offers a simplified, linear algebra-based perspective on Higgs bundles, making the complex subject more accessible to a broader audience.

Findings

Highlights linear algebra aspects of Higgs bundles

Connects linear algebra to the structure of moduli spaces

Aims to promote understanding of Higgs bundles in the mathematical community

Abstract

Higgs bundles appeared a few decades ago as solutions to certain equations from physics and have attracted much attention in geometry as well as other areas of mathematics and physics. Here, we take a very informal stroll through some aspects of linear algebra that anticipate the deeper structure in the moduli space of Higgs bundles. (This note was produced for the MFO Snapshots of Modern Mathematics series, which is "designed to promote the understanding and appreciation of modern mathematics and mathematical research in the interested public world-wide.")