Some current projects (tentative titles!):
A. Moriani, N. Rungi, E. Trebeschi: Ricci curvature of maximal submanifolds (in progress)
G. Faraco, N. Rungi: Branched real projective structures on surfaces (in progress)
C. El Emam, F. Mazzoli, N. Rungi, A. Seppi, A. Tamburelli: A natural complex hyperkähler metric on the space of minimal immersions into PSL(2,C) (in progress)
Preprints:
N. Rungi: Equiaffine immersions and pseudo-Riemannian space-forms arXiv:2512.09569 (Submitted)
N. Rungi, A. Tamburelli: Para-complex geometry and cyclic Higgs bundles arXiv:2503.01615 (Submitted)
N. Rungi, A. Tamburelli: Complex Lagrangian minimal surfaces, bi-complex Higgs bundles and SL(3,C)-quasi-Fuchsian representations arXiv:2406.14945 (Submitted)
Publications:
N. Rungi, A. Tamburelli: The moduli space of flat maximal space-like embeddings in pseudo-hyperbolic space, Annals of Global Analysis and Geometry, Volume 67, Number 15 (2025) ArXiv - Published
N. Rungi, A. Tamburelli: A semi-pseudo-Kähler structure on the SL(3,R)-Hitchin component and the Goldman symplectic form, Advances in Mathematics, Volume 461 (2025) ArXiv - Published
N. Rungi: Riemannian geometry of maximal surface group representations acting on pseudo-hyperbolic space, Mathematische Annalen, Volume 391, pages 4191–4231 (2025) ArXiv - Published
Projections to Teichmüller space, Oberwolfach Report (2022), Volume 19 - Number 4 (pdf, DOI: 10.4171/OWR/2022/47)
N. Rungi, A. Tamburelli: Global Darboux coordinates for complete Lagrangian fibrations and an application to the deformation space of projective structures in genus one, Journal of Symplectic Geometry, Volume 22, Number 2 (2024) ArXiv - Published
N. Rungi, A. Tamburelli: Pseudo-Kähler geometry of properly convex projective structures on the torus, Journal of Geometric Analysis Volume 34, Number 116 (2024) ArXiv - Published
Some notes and slides from past events:
Arbeitsgemeinschaft: Higher Rank Teichmüller Theory, Oberwolfach, Germany, 12/10/2022, (notes)
Geometric Structures (Re)United (poster session), UIL, Chicago, 17/06/2022, (pdf file)
Informal Workshop in Paradiso 2022, Cogne (AO), 03/02/2022, (slides)
Geometry Seminar, SISSA, Trieste, 01/10/2021, (slides)