12
Fachbereich
Institut für Mathematik
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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. More specifically, I would like to understand how the geometry of the singular locus of the Hitchin fibration effects its hyperkähler structure. In this framework, I am doing research concerning the Kapustin-Witten mirror symmetry of special subvarieties (branes) and the asymptotics of the hyperkähler metric. More recently, strata of k-differentials, stability manifolds and wall-crossing phenomena became important players in my research. 

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.

Lehre

Vorkurs Mathematik: 06 - 10. Oktober 2025, weitere Informationen auf der Institutsseite/Studium.

Publications + Preprints

  1. Semi-abelian spectral data for singular fibers of the SL(2,C)-Hitchin system, Int. Math. Res. Not. 2022, No. 5, 3860-3917 (2022), arXiv.
  2. sl(2)-type singular fibres of the symplectic and odd orthogonal Hitchin system, J. Topol. 15, No. 1, 1-38 (2022), arXiv.
  3. (with Martin Möller) Compactifying the rank two Hitchin system via spectral data on semistable curves, Algebr. Geom. 11, No. 6, 849-894 (2024). , arXiv.
  4. (with Johannes Schwab) Visible Lagrangians for Hitchin systems and pillowcase covers, 2023, preprint, arXiv.
  5. (with Emilio Franco, Robert Hanson, André Oliveira) Fourier-Mukai transforms and normalization of nodal curves, 2024, preprint, arXiv.
  6. (with Siqi He and Nianzi Li) The asymptotics of the SL(2,C)-Hitchin metric on the singular locus: subintegrable systems, 2025, preprint, arXiv.
  7. (with Martin Möller) Wall-crossing formulas via spectral networks, 2025, preprint, arXiv.

Talks

  1. Mai 2025: "Asymptotic of the Hitchin metric on subintegrable systems", Conference Stratifications of Higgs bundle moduli spaces, Universidade de Santiago de Compostela. and related topics
  2. Apr. 2024: "Visible Lagrangians in Hitchin systems", Workshop: Advances in Higgs bundles, BRIN center, University of Maryland at College Park.
  3. Nov. 2023: "From Lagrangians in Hitchin systems to pillowcase covers", Geometrieseminar, Universität Heidelberg.
  4. Aug. 2023: "Visibile Lagrangians and square-tiled surfaces", VBAC - Recent applications to the geometry of moduli spaces, Universität Duisburg-Essen.
  5. June 2022: "Singular Hitchin fibers via Hecke modifications and abelianisation", Geometric structures (re)united, University of Illinois at Chicago.
  6. May 2022: "Resolving rank 2 spectral covers by semi-stable curves", Essener Seminar für algebraische Geometrie und Arithmetik, Universität Duisburg-Essen.
  7. Feb. 2022: "Resolving the rank 2 Hitchin system by compactified Jacobians of semi-stable curves", Geometria em Lisboa, Lisbon.
  8. 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.
  9. Nov. 2021: "A modified Hitchin base using quadratic multi-scale differentials", Geometry and Topology Seminar, Universidade do Porto.
  10. Feb. 2021: "Spectral data for singular Hitchin fibers and asymptotic solutions to the Hitchin equation", Complex Analysis Seminar, Freie Universität Berlin.
  11. Jan. 2021: "Singular fibers of the symplectic and odd orthogonal Hitchin system", Geometry and Topology Seminar, Universidade do Porto.
  12. Mar. 2020: "Singular fibers of Hitchin integrable systems", Geometry-Topology Seminar, University of Maryland, College Park.
  13. Feb. 2020: "Singular fibers of Hitchin integrable systems", Seminar Symplectic Geometry, Gauge Theory and Categorification, Columbia University, New York.
  14. Nov. 2018: "Limiting configurations on the singular locus of the Hitchin map", Oberseminar Geometrie at Karl-Albrechts-Universität zu Kiel.

Slides

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

Past Events and Teaching

  • GAUS seminar: Moduli of Quiver Representations and GIT Quotients, WS 24/25, Programm.
  • 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
  • Workshop "Ramification in geometric Langlands and non-abelian Hodge theory", September 9 - 13, 2024, University of Heidelberg, webpage.