- Group leader: Prof. Florent Schaffhauser.
- Affiliation: Institute for Mathematics, Heidelberg University.
- Years active: since 2023.
Research interests
- Higgs bundles.
- Character varieties.
- Gauge theory.
- Moduli spaces.
- Orbifolds and stacks.
- Fuchsian groups.
- Topology of real algebraic varieties.
- Homotopy type theory.
- Formal mathematics.
- Computer-assisted proof.
Team
- Prof. Florent Schaffhauser (Principal investigator).
- Dr. Kevin Klinge (Scientific collaborator)
Former members
- Dr. Tommaso Scognamiglio (Scientific collaborator).
Project collaborators
- Johannes Rau (Universidad de Los Andes).
- Manuel Aragón (Universität Bonn).
- Emanuel Roth (University of Edinburgh).
- Juan Sebastián Numpaque-Roa (Universidade do Porto).
- Luca Dal Molin (Università di Trento).
Funding
- Excellence grant: Mobility in International Research Collaboration, 2024-2026. Project ID: ExU 11.2.1.45. Role: PI.
- AEI-DFG joint Spanish-German research project, 2025-2028. Very-stability, Hecke transforms and representation varieties in the presence of symmetry (V-SHARP). Project ID: SCHA 2147_1-1 AOBJ 706923. Role: PI.
Seminars and Workshops
- Formal Mathematics Seminar (co-organized with Judith Ludwig and Denis Vogel).
- Lean Workshop 2025: Formalising Algebraic Geometry (co-organized with Judith Ludwig).
Activities
- 03.06.2024-20.06.2024: Research visit from Prof. Johannes Rau (Universidad de Los Andes).
- 24.06.2024-30.07.2024: Research visit from Manuel Aragón (Universidad de Los Andes).
- Winter semester 2024/25: RTG Lectures on Vector bundles over Riemann surfaces (F. Schaffhauser).
- 14.11.2024-15.11.2024: HGS-MathComp Compact Course on Interactive Theorem Proving in Lean (F. Schaffhauser).
- 18.11.2024-22.11.2024: CIRM-Luminy Conference on Algebraic Geometry and Complex Geometry (F. Schaffhauser and T. Scognamiglio).
- 02.12.2024-06.12.2024: Mini-course on Mathematics, Logic and Informatics at Universidad de Los Andes (F. Schaffhauser).
- 12.03.2025-13.03.2025: Mini-course on Interactive Theorem Proving in Lean at the Max Planck Institute for Mathematics in the Sciences (F. Schaffhauser).
- 07.04.2025-11.04.2025: Research visit by Emanuel Roth (University of Edinburgh).
- 05.05.2025-09.09.2025: Talk on Hodge bundles with Galois symmetry at the workshop Stratifications of Higgs bundle moduli spaces and related topics, U. Santiago de Compostela.
- Summer semester 2025: RTG Lectures on Local systems on Riemann surfaces and character varieties (T. Scognamiglio).
- 02.06.2025-06.06.2025: Participation in the meeting on Real algebraic geometry and Birational geometry at CIRM in Luminy (F. Schaffhauser).
- 09.06.2025-13.06-2025: Participation in the TYPES 2025 conference at the the University of Strathclyde in Glasgow (F. Schaffhauser).
- 10.07.2025: Felix Lentze defended his Bachelor thesis on Formalizing Dedekind cuts in Lean.
- 07.08.2025: Sebastian Grafe defended his Bachelor thesis on Gaussian elimination in Lean.
- 14.08.2025: Talk on Algebra, Logic, and Proof Visualization at the Illustrating Mathematics: Reunion/Expansion meeeting. ICERM, 11-15.08.2025 (F. Schaffhauser).
- 01.09.2025-05.09.2025: Mini-course on Local systems on Riemann surfaces, character varieties, and non-abelian Hodge theory at Universidad de Los Andes (T. Scognamiglio).
- 22.09.2025: Daniel Geisler defended his Bachelor thesis on Introduction to Dessins d’enfants.
- 06.10.2025-10.10.2025: Tutorial on Interactive Theorem Proving in Lean at the 18th Conference on Intelligent Computer Mathematics in Brasilia (F. Schaffhauser).
- 15.10.2025-15.02.2026: Research visit from Luca Dal Molin (Università di Trento).
- 12.01.2026-16.01.2026: Indo-European Symposium on Diffierential and Complex Geometry, co-organized by F. Schaffhauser and Mainak Poddar (IISER Pune).
Publications
- Daniele Alessandrini, Gye-Seon Lee and Florent Schaffhauser. Hitchin components for orbifolds. J. Eur. Math. Soc. 25 (2023), no. 4, pp. 1285–1347.
- Erwan Brugallé and Florent Schaffhauser. Maximality of moduli spaces of vector bundles on curves. Épijournal de Géométrie Algébrique (EPIGA), Volume 6 (2023).
- Juan Martín Pérez and Florent Schaffhauser. Orbifolds and the modular curve. In Ohshika, K., Papadopoulos, A. (eds) In the Tradition of Thurston III, pp 365–421, Springer (First online: 19 March 2024).
- Tommaso Scognamiglio. Cohomology of non-generic character stacks. Journal de l’École polytechnique — Mathématiques, Volume 11 (2024), pp. 1287-1371
- Florent Schaffhauser, Vincent Voß and Katrin Weiß. Algebra, Logik, und Beweisvisualisierung. Mitteilungen der Deutschen Mathematiker-Vereinigung, vol. 33, no. 3, 2025, pp. 205-209.
- Numpaque-Roa JS, Schaffhauser F. Flat Torsors in Complex Geometry. In: del Ángel R. PL, Neumann F, Schmitt AHW, eds. Moduli, Motives and Bundles: New Trends in Algebraic Geometry. London Mathematical Society Lecture Note Series. Cambridge University Press (2025), pp. 106-142.
Preprints
- Emanuel Roth and Florent Schaffhauser. Harder-Narasimhan filtrations of decorated vector bundles. arXiv:2511.17371.
- Florent Schaffhauser and Tommaso Scognamiglio. Real Bialynicki-Birula flows in moduli spaces of Higgs bundles. arXiv:2507.18613.
Job openings
Post-Doctoral position
This position has now been filled.