Dr. Johannes Horn

I am a Postdoc of CRC 326 - GAUS in the reserach group of Prof. Martin Möller.

I am interested in the complex algebraic and symplectic geometry of Higgs bundle moduli spaces and related topics. More recently, I am studying mirror symmetry questions about Higgs bundle moduli spaces and new approaches to compatified Jacobians and Prym varieties using logarithmic geometry. 

I did my PhD on the topic "Singular fibres of Hitchin systems" at Ruprecht-Karl Universität Heidelberg under supervision of Dr. Daniele Alessandrini and Prof. Dr. Anna Wienhard.

You can find more details in my curriculum vitae.


Vorkurs Mathematik: 08. - 12. April 2024, weitere Informationen auf der Institutsseite/Studium

Workshop "Ramification in geometric Langlands and non-abelian Hodge theory"

September 9 - 13, 2024, University of Heidelberg, webpage.

This workshop is motivated by recent developments in geometric representation theory, related to wild ramification in the geometric Langlands program and non-abelian Hodge theory. The goal is to bring together researchers in these fields and researchers on irregular singularities (in particular Stokes phenomena), to stimulate future interactions.


  • Semi-abelian spectral data for singular fibers of the SL(2,C)-Hitchin system, Int. Math. Res. Not. (10) 2020, ISSN 1073-7928, eprint.
  • sl(2)-type singular fibres of the symplectic and odd orthogonal Hitchin system, Journal of Topology, Vol. 15, Iss. 1 2022, eprint.


  • (with Martin Möller) Compactifying the rank two Hitchin system via spectral data on semistable curves, 2022, to appear in Algebraic Geometry, eprint.
  • (with Johannes Schwab) Visible Lagrangians for Hitchin systems and pillowcase covers, 2023, eprint.
  • (with Emilio Franco, Robert Hanson, André Oliveira) Fourier-Mukai transforms and normalization of nodal curves, 2024, eprint.


  1. Apr. 2024: "Visible Lagrangians in Hitchin systems", Workshop: Advances in Higgs bundles, BRIN center, University of Maryland at College Park.
  2. Nov. 2023: "From Lagrangians in Hitchin systems to pillowcase covers", Geometrieseminar, Universität Heidelberg.
  3. Aug. 2023: "Visibile Lagrangians and square-tiled surfaces", VBAC - Recent applications to the geometry of moduli spaces, Universität Duisburg-Essen.
  4. June 2022: "Singular Hitchin fibers via Hecke modifications and abelianisation", Geometric structures (re)united, University of Illinois at Chicago.
  5. May 2022: "Resolving rank 2 spectral covers by semi-stable curves", Essener Seminar für algebraische Geometrie und Arithmetik, Universität Duisburg-Essen.
  6. Feb. 2022: "Resolving the rank 2 Hitchin system by compactified Jacobians of semi-stable curves", Geometria em Lisboa, Lisbon.
  7. Dec. 2021: "Compactifying the GL(2,C)-Hitchin system on the space of quadratic multi-scale differentials", Workshop: Higgs bundles at infinity, Karl-Albrechts-Universität zu Kiel.
  8. Nov. 2021: "A modified Hitchin base using quadratic multi-scale differentials", Geometry and Topology Seminar, Universidade do Porto.
  9. Feb. 2021: "Spectral data for singular Hitchin fibers and asymptotic solutions to the Hitchin equation", Complex Analysis Seminar, Freie Universität Berlin.
  10. Jan. 2021: "Singular fibers of the symplectic and odd orthogonal Hitchin system", Geometry and Topology Seminar, Universidade do Porto.
  11. Mar. 2020: "Singular fibers of Hitchin integrable systems", Geometry-Topology Seminar, University of Maryland, College Park.
  12. Feb. 2020: "Singular fibers of Hitchin integrable systems", Seminar Symplectic Geometry, Gauge Theory and Categorification, Columbia University, New York.
  13. Nov. 2018: "Limiting configurations on the singular locus of the Hitchin map", Oberseminar Geometrie at Karl-Albrechts-Universität zu Kiel.


  • Oct. 2020: "Defense of Thesis: Singular fibers of Hitchin systems", Ruprecht-Karl-Universität Heidelberg, Slides.

Past Events and Teaching

  • Vorlesung Lie-Gruppen und algebraische Gruppen, WS 23/24, Montag 12-14 Uhr & Donnerstag 10-12 Uhr, Raum 308. Weitere Information auf der Vorlesungswebseite.
  • Workshop series "The geometry of sheaves: From derived categories to Higgs bundles", SS 2022 - SS 2023, webpage.
  • "What is ...???"-coffee break seminar, SS 2021-WS 2021/22.
  • Forschungsseminar DaFraHeiMai/GAUS-Seminar SS 2021: The P=W conjecture.
  • Exercise Session: Geometric Group Theory, WS 2020/2021, Prof. Möller
  • Vorkurs Mathematik für Mathematikstudierende: WS 2022/23, SS 2023, WS 2023/24


Dr. Johannes Horn
FB 12 - Institut für Mathematik

Johann Wolfgang Goethe-Universität
Robert-Mayer-Str. 6-8
D-60325 Frankfurt am Main

Phone: +49-69-798-22326
E-mail: horn[add-at]math.uni-frankfurt.de

Office: 212