- 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 Differential and Complex Geometry, co-organized by F. Schaffhauser and Mainak Poddar (IISER Pune).
- 09.03.2026-29.03.2026: JSPS Bridge Fellowship at the University of Tokyo (F. Schaffhauser). Invited talk on Moduli of vector bundles over real algebraic curves at the Mathematical Society of Japan Spring Meeting 2026.
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.