Research

Mathematics in Heidelberg

The Heidelberg Experimental Geometry Lab (HEGL) is part of the Research Station Geometry+Dynamics, which is part of the Institute for Mathematics, which is part of the Faculty of Mathematics and Computer Science at Heidelberg University.

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 Juan Martín Pérez. 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).  
2. With Daniele Alessandrini and Gye-Seon Lee. Hitchin components for orbifolds.
   J. Eur. Math. Soc. 25 (2023), no. 4, pp. 1285–1347.  
3. With Erwan Brugallé. Maximality of moduli spaces of vector bundles on curves.  
   Épijournal de Géométrie Algébrique (EPIGA), Volume 6 (2023).  
4. Symmetric differentials and the dimension of Hitchin components for orbi-curves. 
   Current Trends in Analysis, its Applications and Computation, Birkhäuser Trends in Mathematics (2022), pp. 129-140.  
5. With Victoria Hoskins. Rational points of quiver moduli spaces.
   Ann. Inst. Fourier Volume 70 (2020) no. 3, pp. 1259–1305.  
6. With Indranil Biswas. Parabolic vector bundles on Klein surfaces.
   Illinois J. Math. 64 (2020), no. 1, pp.105–118.  
7. With Victoria Hoskins. Group actions on quiver varieties and applications.
   Internat. J. Math. 30 (2019), no. 2, p. 1950007, 46.  
8. Finite group actions on moduli spaces of vector bundles.
   Sémin. Théor. Spectr. Géom. (Grenoble) 34 (2016-2017), 33–63.  
9. On the Narasimhan-Seshadri correspondence for Real and Quaternionic vector bundles.
   J. Differential Geom. (2017) 105 (1), 119–162.  
10. 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.  
11. With Indranil Biswas. Vector bundles over a real elliptic curve.
    Pacific J. Math. (2016) 283 (1), 43–62.  
12. 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.  
13. With Chiu-Chu Melissa Liu. The Yang-Mills equations over Klein surfaces.
    J. Topol. (2013) 6 (3), 569–643.  
14. Real points of coarse moduli schemes of vector bundles on a real algebraic curve.
    J. Symplectic Geom. 10 (2012), no. 4, 503–534.  
15. Moduli spaces of vector bundles over a Klein surface.
    Geom. Dedicata 151 (2011), no. 1, 187–206.  
16. Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups.
     Math. Ann. 342 (2008), no. 2, 405–447.  
17. Anti-symplectic involutions on quasi-Hamiltonian quotients.
    Trav. Math. 17 (2007) 57–64.  
18. A note on quasi-Hamiltonian geometry and representation spaces of surface groups.
    Sem. Math. Sci. 36 (2007), 35–48.  
19. 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).  
20. 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.  
21. 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.  
22. 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.