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.

Lehre

  • Vorkurs Mathematik: 09. - 13. Oktober 2023, weitere Informationen auf der Institutsseite/Studium.
  • 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"

We are organizing a series of one-day workshops at Frankfurt university in summer term 2022 covering topics in the realm of moduli spaces of vector- and Higgs bundles, representation varieties and non-abelian Hodge theory. You can find more information here .

Publications

  • 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.

Preprints

  • (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.

Talks

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

  • "What is ...???"-coffee break seminar, SS 2021-WS 2021/22.
  • Forschungsseminar DaFraHeiMai/GAUS-Seminar SS 2021: The P=W conjecture
    Do., 15.00-18.00 Uhr
  • Exercise Session: Geometric Group Theory, WS 2020/2021, Prof. Möller
  • Vorkurs Mathematik für Mathematikstudierende: WS 2022/23, SS 2023

Kontakt

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