Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 029, 34 pages      arXiv:1908.08348      https://doi.org/10.3842/SIGMA.2020.029
Contribution to the Special Issue on Integrability, Geometry, Moduli in honor of Motohico Mulase for his 65th birthday

Non-Abelian Hodge Theory and Related Topics

Pengfei Huang ab
a)  School of Mathematics, University of Science and Technology of China, Hefei 230026, China
b)  Laboratoire J.A. Dieudonné, Université Côte d'Azur, CNRS, 06108 Nice, France

Received August 23, 2019, in final form April 08, 2020; Published online April 19, 2020

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.

Key words: non-Abelian Hodge theory; $\lambda$-connection; moduli space; conformal limit; Hitchin section; oper; stratification; twistor space.

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