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    Prof Dr Maria Beatrice Pozzetti

    Office 3/309, 3rd floor
    Mathematical Institute
    Heidelberg University
    Im Neuenheimer feld 205
    69120 Heidelberg
    Germany

    Tel: +49-(0)6221-54 14206


 Email: pozzetti@mathi.uni-heidelberg.de

I am head of an Emmy-Noether research group on Discrete subgroups of semisimple Lie groups beyond Anosov

With the project Rigidity, deformations and limits of maximal representations I am part of the DFG priority program SPP 2026 Geometry at infinity

With the projects A8: Symplectic geometry of representation and quiver varieties and B5: hyperbolicity in dynamics and geometry I am part of the DFG CRC/TRR 191: Symplectic structures in geometry, algebra and dynamics

I am PI of the RTG 2229: Asymptotic Invariants and Limits of Groups and Spaces

I am co-organizing Heidelberg's Differential geometry seminar

Group members:

  1. Valdo Tatitscheff (Postdoc)
  2. Alexander Thomas (Postdoc)
  3. Marta Magnani (PhD student)
  4. Colin Davalo (PhD student)

Former group members:

  1. Mitul Islam (Postdoc)
  2. Giulio Belletti (Postdoc)
  3. James Farre (Postdoc)
  4. Leon Carvajales (Postdoc)
  5. Gabriele Viaggi (Postdoc)

Research interests: Discrete subgroups of semisimple Lie groups, Anosov and maximal representations, (complex) hyperbolic geometry, (Higher rank) Teichmüller-Thurston Theory, geometric group theory, bounded cohomology

Published/accepted papers:

  1. (with L. Carvajales, X. Dai, A. Wienhard) Thurston's asymmetric metrics for Anosov representations.
    Accepted in Groups Geometry Dynamics arXiv:2210.05292
  2. (with M. Burger, A. Iozzi, A. Parreau) Weyl chamber length compactification of the PSL(2,R)xPSL(2,R) maximal character variety.
    Accepted in Glasgow Math J. arXiv:2112.13624
  3. (with K. Tsouvalas) On projective Anosov subgroups of symplectic groups.
    Bull. London Math. Soc., 56: 581-588 (2024) arXiv:2305.05018
  4. (with M. Burger, A. Iozzi, A. Parreau) Positive crossratios, barycenters, trees and applications to maximal representations.
    Accepted in Groups, Geometry, and Dynamics. arXiv:2103.17161
  5. (with A. Sambarino, A. Wienhard) Anosov representations with Lipschitz limit set.
    Geometry & Topology 27-8 (2023), 3303--3360 arXiv:1910.06627
  6. (with M.Bridgeman, A. Sambarino, A. Wienhard) Hessian of Hausdorff dimension on purely imaginary directions.
    Bull. Lond. Math. Soc. 54, 3 (2022) 1027-1050 arXiv:2010.16308
  7. (with B. Duchesne, J. Lecureux) Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces.
    Ergod. Th. & Dynam. Sys., (2023), 43, 140-189 arXiv:1810.10208
  8. (with S. Maloni) Geometric limits of cyclic subgroups of SO(1, k+1) and SU(1, k+1).
    Algebraic & Geometric Topology 22 (2022) 1461-1495 arXiv:2008.11653
  9. (with M. Burger, A. Iozzi, A. Parreau) Currents, Systoles, and Compactifications of Character Varieties.
    Proc. London Math. Soc.(3) 123 (2021) 565-596 arXiv:1902.07680
  10. (with J. Beyrer) A collar lemma for partially hyperconvex surface group representations.
    Trans. Amer. Math. Soc. 374 (2021), 6927-6961 arXiv:2004.03559
  11. (with M. Burger, A. Iozzi, A. Parreau) The real spectrum compactification of character varieties: characterizations and applications.
    Comptes Rendus. Mathematique, Tome 359 (2021) no. 4, pp. 439-463. pdf
  12. (with A. Sambarino, A. Wienhard) Conformality for a robust class of non-conformal attractors.
    Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2021, no. 774, 2021, pp. 1-51 pdf
  13. (with F. Fanoni) Basmajian-type inequalities for maximal representations.
    Journal of Differential Geometry, Vol. 116, No. 3 (2020), pp. 405-458. pdf
  14. (with F. Franceschini, R. Frigerio, A. Sisto) The zero norm subspace of bounded cohomology of acylindrically hyperbolic groups.
    Commentarii Mathematici Helvetici 94-1 (2019), 89--139 pdf
  15. (with M. Burger) Maximal representations, non Archimedean Siegel spaces, and buildings.
    Geometry & Topology 21-6 (2017), 3539--3599 pdf
  16. Boundary maps and maximal representations of complex hyperbolic lattices into SU(m,n).
    PhD Thesis, ETH Zurich pdf
  17. Maximal representations of complex hyperbolic lattices into SU(m, n).
    Geom. Funct. Anal. 25 (2015), no. 4, 1290–1332 pdf
  18. (with R. Frigerio, A. Sisto) Extending higher dimensional quasi-cocycles.
    J. Topol. 8 (2015), no. 4, 1123–1155 pdf
  19. (with M. Bucher, M. Burger, R. Frigerio, A. Iozzi, C. Pagliantini) Isometric properties of relative bounded cohomology.
    J. Topol. Anal. 6 (2014), no. 1, 1-25.

Conference papers:

  1. (with F. Lopez, S. Trettel, M. Strube, A. Wienhard) Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices.
    In Proceedings of the Thirty-fifth Conference on Neural Information Processing Systems (NeurIPS 2021) arXiv:2110.13475
  2. (with F. Lopez, S. Trettel, M. Strube, A. Wienhard) Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach.
    In Proceedings of the 38th International Conference on Machine Learning (ICML 2021) arXiv:2106.04941

Preprints:

  1. (with J. Farre, G. Viaggi) Topological and geometric restrictions on hyperconvex representations.
    Preprint. Available online: arXiv:2403.13668
  2. (with M. Burger, A. Iozzi, A. Parreau) The real spectrum compactification of character varieties.
    Preprint. Available online: arXiv:2311.01892
  3. (with A. Sambarino) Metric properties of boundary maps, Hilbert entropy and non-differentiability.
    Preprint. Available online: arXiv:2310.07373
  4. (with J. Beyrer) Positive surface group representations in PO(p,q).
    Preprint. Available online: arXiv:2106.14725
  5. (with J. Beyrer) Degenerations of k-positive surface group representations.
    Preprint. Available online: arXiv:2106.05983
  6. (with O. Hamlet) Classification of tight homomorphisms.
    Preprint. Available online: arXiv:1412.6398

Expository/notes:

  1. Higher rank Teichmüller theories Exposé 1161 in the Séminaire N. Bourbaki (Mars 2019)
  2. Compactifications via affine buildings Notes for the Workshop on compactifications of moduli spaces of representations
  3. Maximal representations Notes for the Workshop on Sp(4,R)-Anosov representations
  4. Maximal representations of complex hyperbolic lattices Oberwolfach reports 30 (2015)
  5. Bounded cohomology and the simplicial volume of the product of two surfaces Master Thesis (2011)

Service:

I am co-organizer of

Teaching in Heidelberg:

Past teaching:

Student supervision:

  • PhD theses:
  • Master theses:
  • Bachelor theses:
  • 4th year projects (Warwick):