Algebra und Geometrie
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Dr. Johannes Horn
I am a Postdoc of CRC 326 - GAUS in the reserach group of Prof. Martin Möller.
My interests lie in complex and differential geometry. More precisely, I am interested in Higgs Bundles, Hitchin Systems, Harmonic Maps and Representations of Surface Groups.
I did my PhD on the topic "Singular fibres of Hitchin systems" at Karl-Ruprecht Universität Heidelberg under supervision of Dr. Daniele Alessandrini and Prof. Dr. Anna Wienhard.
You can find more details in my curriculum vitae.
E-Mail: horn [at] math.uni-frankfurt.de
Publications
- Semi-abelian spectral data for singular fibers of the SL(2,C)-Hitchin system, Int. Math. Res. Not., Vol. 2022, Issue 5, March 2022, eprint .
Preprints
- sl(2)-type singular fibres of the symplectic and odd orthogonal Hitchin system, 2020, accepted for publication by the Journal of Topology, eprint .
- (with Martin Möller) Compactifying the rank two Hitchin system via spectral data on semistable curves, 2022, eprint .
Invited talks
- Feb. 2022: "Resolving the rank 2 Hitchin system by compactified Jacobians of semi-stable curves", Geometria em Lisboa, Lisbon.
- 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.
- Nov. 2021: "A modified Hitchin base using quadratic multi-scale differentials", Geometry and Topology Seminar, Universidade do Porto.
- Feb. 2021: "Spectral data for singular Hitchin fibers and asymptotic solutions to the Hitchin equation", Complex Analysis Seminar, Freie Universität Berlin.
- Jan. 2021: "Singular fibers of the symplectic and odd orthogonal Hitchin system", Geometry and Topology Seminar, Universidade do Porto.
- Mar. 2020: "Singular fibers of Hitchin integrable systems", Geometry-Topology Seminar, University of Maryland, College Park.
- Feb. 2020: "Singular fibers of Hitchin integrable systems", Seminar Symplectic Geometry, Gauge Theory and Categorification, Columbia University, New York.
- 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
- Forschungsseminar DaFraHeiMai/GAUS-Seminar SS 2021:
The P=W conjecture
Do., 15.00-18.00 Uhr