Non-Abelian Hodge Theory and Related Topics

TL;DR

This survey introduces non-Abelian Hodge theory, explaining the correspondence between flat and Higgs bundles, and discusses recent advances in moduli space studies and open problems in the field.

Contribution

It provides an accessible overview of non-Abelian Hodge theory and highlights recent developments and open problems in the study of related moduli spaces.

Findings

Overview of the correspondence between flat and Higgs bundles

Recent progress in moduli space research

Identification of open problems in the field

Abstract

This paper is a survey aimed on the introduction of non-Abelian Hodge theory that gives the correspondence between flat bundles and Higgs bundles. We will also introduce some topics arising from this theory, especially some recent developments on the study of the relevant moduli spaces together with some interesting open problems.