Higgs bundles without geometry

@article{Rayan2020HiggsBW,
  title={Higgs bundles without geometry},
  author={Steven Rayan and Laura P. Schaposnik},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}
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… 

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References

SHOWING 1-7 OF 7 REFERENCES

Aspects of the Topology and Combinatorics of Higgs Bundle Moduli Spaces

  • S. Rayan
  • Mathematics
    Symmetry, Integrability and Geometry: Methods and Applications
  • 2018
This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how

THE SELF-DUALITY EQUATIONS ON A RIEMANN SURFACE

In this paper we shall study a special class of solutions of the self-dual Yang-Mills equations. The original self-duality equations which arose in mathematical physics were defined on Euclidean

Le lemme fondamental pour les algebres de Lie

We propose a proof for conjectures of Langlands, Shelstad and Waldspurger known as the fundamental lemma for Lie algebras and the non-standard fundamental lemma. The proof is based on a study of the

Stable bundles and integrable systems

On considere la geometrie symplectique des fibres cotangents aux espaces de modules de fibres vectoriels stables sur une surface de Riemann. On montre que ce sont des systemes dynamiques hamiltoniens

Advanced topics in gauge theory: geometry and physics of Higgs bundles, to appear in Park City Mathematics Series, AMS (2019)

  • 1995

Riemann surfaces and integrable systems. Notes by Justin Sawon

  • Oxf. Grad. Texts Math. 4, Integrable Systems: Twistors, Loop Groups, and Riemann surfaces (Oxford,
  • 1997

Riemann surfaces and integrable systems

  • Integrable Systems: Twistors, Loop Groups, and Riemann surfaces
  • 1997