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Florent Schaffhauser

Pic_Flo

Vertretungsprofessor (interim professor)
Faculty of Mathematics and Computer Science
Ruprecht-Karls-Universität Heidelberg

Research

Research interests

My research interests lie in the area at the intersection of algebraic and differential geometry. I study Galois and hidden symmetries of Yang-Mills connections, with applications to the topology and geometry of real and complex algebraic varieties.

  • Fuchsian groups (30F35)
  • Vector bundles on curves and their moduli (14H60)
  • Special connections and metrics on vector bundles (53C07)
  • Topology of real algebraic varieties (14P25)

Publications

  1. With Erwan Brugallé. Maximality of moduli spaces of vector bundles on curves.  
    To appear in EPIGA.  
  2. Symmetric differentials and the dimension of Hitchin components for orbi-curves. 
    In Proceedings of the ISAAC 2019 Congress (Aveiro). To appear.  
  3. With Daniele Alessandrini and Gye-Seon Lee. Hitchin components for orbifolds.
    J. Eur. Math. Soc. Published online first: 14-02-2022.
  4. With Victoria Hoskins. Rational points of quiver moduli spaces.
    Ann. Inst. Fourier Volume 70 (2020) no. 3, pp. 1259–1305.
  5. With Indranil Biswas. Parabolic vector bundles on Klein surfaces.
    Illinois J. Math. 64 (2020), no. 1, pp.105–118.
  6. With Victoria Hoskins. Group actions on quiver varieties and applications.
    Internat. J. Math. 30 (2019), no. 2, p. 1950007, 46.
  7. Finite group actions on moduli spaces of vector bundles.
    Sémin. Théor. Spectr. Géom. (Grenoble) 34 (2016-2017), 33–63.
  8. On the Narasimhan-Seshadri correspondence for Real and Quaternionic vector bundles.
    J. Differential Geom. (2017) 105 (1), 119–162.
  9. Lectures on Klein surfaces and their fundamental group.  In Geometry and Quantization of Moduli Spaces.   Advanced Courses in Mathematics - CRM Barcelona. Springer (2016), 67–108.  
  10. With Indranil Biswas. Vector bundles over a real elliptic curve.
    Pacific J. Math. (2016) 283 (1), 43–62.
  11. Differential geometry of holomorphic vector bundles on a curve. In Geometric and Topological Methods for Quantum Field Theory. Proceedings of the 2009 Villa de Leyva Summer School. Cambridge University Press (2013), 39–80.  
  12. With Chiu-Chu Melissa Liu. The Yang-Mills equations over Klein surfaces.
    J. Topol. (2013) 6 (3), 569–643.
  13. Real points of coarse moduli schemes of vector bundles on a real algebraic curve.
    J. Symplectic Geom. 10 (2012), no. 4, 503–534.
  14. Moduli spaces of vector bundles over a Klein surface.
    Geom. Dedicata 151 (2011), no. 1, 187–206.
  15. Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups.
     Math. Ann. 342 (2008), no. 2, 405–447.
  16. Anti-symplectic involutions on quasi-Hamiltonian quotients.
    Trav. Math. 17 (2007) 57–64.
  17. A note on quasi-Hamiltonian geometry and representation spaces of surface groups.
    Sem. Math. Sci. 36 (2007), 35–48.  
  18. Quasi-Hamiltonian quotients as disjoint unions of symplectic manifolds.  In Non-Commutative Geometry and Physics 2005.   Proceedings of the 2005 International Sendai-Beijing Joint Workshop, 31-54. World Scientific Press(2007).  
  19. Un théorème de convexité réel pour les applications moment à valeurs dans un groupe de Lie. C. R. Math. Acad. Sci. Paris 345 (2007), no. 1, 25–30.
  20. Representations of the fundamental group of an L-punctured sphere generated by products of Lagrangian involutions.
    Canad. J. Math. 59 (2007), no. 4, 845–879.
  21. With Elisha Falbel and Jean-Pierre Marco. Classifying triples of Lagrangians in a Hermitian vector space.
    Topology Appl. 144 (2004), no. 1-3, 1–27.

Preprints and other material

  • Habilitation Thesis: Topology of representation varieties of Fuchsian groups (2019).  
  • Coco's Fest 2016: Categorías abelianas con conjugación (Bogotá, 2016).  
  • 50 years of the Narasimhan-Seshadri theorem: Real Seifert manifolds and the Narasimhan-Seshadri correspondence (NS@50, Chennai 2015).  
  • The Yang-Mills equations over Klein surfaces (Seoul ICM 2014, contributed talk).  
  • Monodromy of Knizhnik-Zamolodchikov equations (2007).  
  • Doctoral Thesis: Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surfaces groups (2005).  

Teaching

Winter Semester 2022-2023

Online resources

Past courses

  • Algebraic topology 1
  • Algebraic topology 2
  • Complex analysis
  • Differential equations
  • Differential geometry 1
  • Geometric invariant theory
  • Measure theory
  • Riemann surfaces
  • Symplectic geometry
  • Vector calculus

Lecture notes, books and other material

  • Lectures on Klein surfaces and their fundamental group
  • Differential geometry of holomorphic vector bundles on a curve.
  • Analyse L3. Pearson Education France (2009). ISBN 9782744073502.  
  • El plano hiperbólico, de la geometría a la teoría de números   (submitted).
  • MCA 2017: A report on the Gender and Mathematics Panel   for the Colombian Society of Mathematics.
  • Congreso Internacional de Matemáticos 2014. Hipótesis 17 (2014), 17-18.  

Students

Under construction

Contact
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