An Introduction to Higgs Bundles via Harmonic Maps

TL;DR

This survey explores the role of equivariant harmonic maps in Higgs bundles, explaining the non-abelian Hodge correspondence and reviewing recent progress on open problems in the field.

Contribution

It provides a comprehensive overview of equivariant harmonic maps in Higgs bundles and discusses recent advances and open problems in the area.

Findings

Clarified the role of harmonic maps in non-abelian Hodge theory

Reviewed progress on open problems in equivariant harmonic maps

Connected harmonic maps with Higgs bundle theory

Abstract

This survey studies equivariant harmonic maps arising from Higgs bundles. We explain the non-abelian Hodge correspondence and focus on the role of equivariant harmonic maps in the correspondence. With the preparation, we review current progress towards some open problems in the study of equivariant harmonic maps.