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

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 J. Beyrer) Degenerations of k-positive surface group representations.
   Journal of Topology 17 (2024) nr. 3 arXiv:2106.05983
2. (with L. Carvajales, X. Dai, A. Wienhard) Thurston's asymmetric metrics for Anosov representations.
   Accepted in Groups Geometry Dynamics arXiv:2210.05292
3. (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
4. (with K. Tsouvalas) On projective Anosov subgroups of symplectic groups.
   Bull. London Math. Soc., 56: 581-588 (2024) arXiv:2305.05018
5. (with M. Burger, A. Iozzi, A. Parreau) Positive crossratios, barycenters, trees and applications to maximal representations.
   Groups Geom. Dyn. 18 (2024), no. 3, pp. 799-847 arXiv:2103.17161
6. (with A. Sambarino, A. Wienhard) Anosov representations with Lipschitz limit set.
   Geometry & Topology 27-8 (2023), 3303--3360 arXiv:1910.06627
7. (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
8. (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
9. (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
10. (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
11. (with J. Beyrer) A collar lemma for partially hyperconvex surface group representations.
    Trans. Amer. Math. Soc. 374 (2021), 6927-6961 arXiv:2004.03559
12. (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
13. (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
14. (with F. Fanoni) Basmajian-type inequalities for maximal representations.
    Journal of Differential Geometry, Vol. 116, No. 3 (2020), pp. 405-458. pdf
15. (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
16. (with M. Burger) Maximal representations, non Archimedean Siegel spaces, and buildings.
    Geometry & Topology 21-6 (2017), 3539--3599 pdf
17. Boundary maps and maximal representations of complex hyperbolic lattices into SU(m,n).
    PhD Thesis, ETH Zurich pdf
18. Maximal representations of complex hyperbolic lattices into SU(m, n).
    Geom. Funct. Anal. 25 (2015), no. 4, 1290–1332 pdf
19. (with R. Frigerio, A. Sisto) Extending higher dimensional quasi-cocycles.
    J. Topol. 8 (2015), no. 4, 1123–1155 pdf
20. (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 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

• the conference Homogeneous dynamics and geometry in higher rank Lie groups (IHES, June 19-23 2023) with M. Bridgeman, D. Canary, F. Kassel, H. Oh, J.F. Quint
• the conference Groups and Dynamics in Geometry (Ascona, May 28-June 2 2023) with H. Baik, M. Bestvina, S. Hensel, A. Iozzi, H. Masur and B. Petri
• the workshop Minimal surfaces in symmetric spaces and Labourie's conjecture (Autrans, August 22-August 26, 2022) with A. Seppi and J. Toulisse
• the conference Marc Burger's Prime (Zurich, June 27-July 1, 2022) with M. Bucher, A. Iozzi, N. Monod and A. Wienhard
• the Mini-Workshop Anosov^3 (Oberwolfach, December 5-11, 2021) with B. Küster, C. Guillarmou and T. Weich
• the conference Geometric Analysis meets Geometric Topology (Heidelberg, February 25-28, 2019) with E. Mäder-Baumdicker, V. Disarlo, F. Fanoni and F. Dittberner
• the conference Groups, spaces and geometries, in honor of Alessandra Iozzi (Zurich, January 22-25, 2019) with C. Burrin, T. Hartnick, E. Kowalski and A. Wienhard
• the GEAR Junior Retreat (Stanford, August 1-7, 2017) with S. Ballas, S. Kerckhoff, T. Yang and T. Zhang
• the conference Asymptotic Geometry of groups and spaces (Heidelberg, February 20-23, 2017) with D. Alessandrini, R. Sauer, P. Schwer and A. Wienhard.

Teaching in Heidelberg:

• Winter 2023/2024: Seminar: Hyperbolische Geometrie
• Sommer 2023: (Pro)Seminar: Konvexgeometrie
• Winter 2021/2022: Lecture: Einfürung in die Geometrie
• Winter 2021/2022: Lecture: Geometrische Gruppentheorie
• Sommer 2021: Seminar: Dynamics in one complex variable
• Winter 2020/2021: Lecture: Differential geometry 2 (Symmetric spaces)
• Winter 2020/2021: Working Seminar: Bridgeland's stability conditions for meromorphic differentials
• Sommer 2020: Lecture: Translation Surfaces
• Winter 2019/2020: Lecture: Geometrische Gruppentheorie
• Winter 2018/2019: Lecture: Differential geometry 2 (Symmetric spaces)
• Sommer 2018: Seminar: Groups acting on trees
• Sommer 2018: Bachelor-Master Seminar
• Winter 2017/2018: Lecture: Differential geometry 2 (Symmetric spaces)
• Sommer 2017: Seminar: The arithmetics of the hyperbolic plane
• Sommer 2017: Junior Geometry Seminar
• Sommer 2017: RTG lecture: Incidence structures on flag varieties and rigidity

Past teaching:

Bonn:
• Sommer 2019: Lecture: V4D4 - Advanced Geometry II
• Sommer 2019: Seminar: S4D1 - Graduate Seminar on Differential Geometry

Warwick University
• Fall and Spring 2016-2017: Organizer of the Geometry and Topology seminar

ETH
• Spring 2012 Running exercise classes for Linear Algebra 2
• Fall 2012 Running exercise classes for Complex analysis
• Fall 2013 Organizing Exercise classes for Algebra (Prof. Brent Doran)
• Spring 2014 Running exercise classes for Algebra 2
• Fall 2014 Organizing and running exercise classes for Algebraic Topology (Prof. Rahul Pandharipande)
• Fall 2014 Organizing the student seminar Geometric group theory 2 (with Alessandro Sisto)

Student supervision: