Research

Lie groupoids and Lie algebroids, Poisson geometry, and their applications to classical geometry: G‑structures, foliations, Lie pseudogroups and the geometry of PDEs.

Papers

• A note on Chern–Weil classes of Cartan connections with L. Accornero and M. M. de Melo Differential Geom. Appl. 103 (2026), article 102365 arXiv:2505.00247 · journal
• The closure of linear foliations with M. M. de Melo Proc. Amer. Math. Soc. 154 (2026), 1755–1762 arXiv:2501.19103 · journal
• Deformations of symplectic groupoids with C. C. Cárdenas and J. N. Mestre Trans. Amer. Math. Soc. 379 (2026), no. 2, 1371–1433 arXiv:2103.14008 · journal
• The global solutions to a Cartan’s realization problem with R. L. Fernandes Mem. Amer. Math. Soc. 306 (2025), no. 1548 arXiv:1907.13614 · journal
• Lie groupoids and semi-local models of singular Riemannian foliations with M. M. Alexandrino, M. K. Inagaki and M. M. de Melo Ann. Global Anal. Geom. 61 (2022), no. 3, 593–619 arXiv:1812.03614 · journal
• The classifying Lie algebroid of a geometric structure II: G‑structures with connection with R. L. Fernandes São Paulo J. Math. Sci. 15 (2021), no. 2, 524–570 arXiv:2107.01193 · journal
• Deformations of Lie groupoids with M. Crainic and J. N. Mestre Int. Math. Res. Not. IMRN 2020, no. 21, 7662–7746 arXiv:1510.02530 · journal
• Stability of Lie group homomorphisms and Lie subgroups with C. C. Cárdenas J. Pure Appl. Algebra 224 (2020), no. 3, 1280–1296 arXiv:1812.03276 · journal
• Multiplicative forms and Spencer operators with M. Crainic and M. A. Salazar Math. Z. 279 (2015), no. 3–4, 939–979 arXiv:1210.2277 · journal
• A survey on stability and rigidity results for Lie algebras with M. Crainic and F. Schätz Indag. Math. 25 (2014), no. 5, 957–976 arXiv:1307.7979 · journal
• The classifying Lie algebroid of a geometric structure I: classes of coframes with R. L. Fernandes Trans. Amer. Math. Soc. 366 (2014), no. 5, 2419–2462 arXiv:1103.5850 · journal
• On the linearization theorem for proper Lie groupoids with M. Crainic Ann. Sci. Éc. Norm. Supér. 46 (2013), no. 5, 723–746 arXiv:1103.5245 · journal
• On Zeeman topology in Kaluza–Klein and gauge theories with M. A. F. Rosa Hadronic J. 32 (2009), no. 2, 221–229 arXiv:math-ph/0504071
• Lie algebroids and classification problems in geometry with R. L. Fernandes São Paulo J. Math. Sci. 2 (2008), no. 2, 263–283 arXiv:0712.3198 · journal

Talks

Recent talks.

• Aug 2026 Lie theory and Cartan’s realization problem — Symposium on Contemporary Differential Geometry at USP, 7th BRICS Mathematics Conference, IME-USP, São Paulo.
• Aug 2026 A Lie theoretic approach to moduli problems in differential geometry (plenary lecture) — Poisson 2026, International Conference on Poisson Geometry, KU Leuven.
• Mar 2026 Chern–Weil classes of Cartan connections — Inaugural Workshop of the Centro Brasileiro de Geometria, IMECC-UNICAMP, Campinas.
• Nov 2025 On geometric structures with regular symmetry pseudogroups — São Paulo Meeting on Geometry (EPG 2025), IME-USP, São Paulo.

Students and postdocs

Postdoctoral researchers

• Luca Accornero, since 2025
• Bruno Suzuki, 2022–2024
• Mateus Moreira de Melo, until 2023
• João Nuno Mestre, until 2020

PhD students

• Laura Ribeiro dos Santos, since 2026
• Beatriz de Faria, since 2026
• Luiz Felipe Villar Fushimi, 2024. Cartan structure groupoids and algebroids
• Cristián Camilo Cárdenas, 2018. Deformation problems for Lie groupoids
• Genaro Pablo Zamudio Chauca, 2018. A generalisation of Γ‑structures

MSc students

• Caio Domiciano Pires dos Santos, since 2026
• Gustavo Bezerra Silva, since 2026
• Bianca Carvalho de Oliveira, 2025. Rational homotopy theory
• Sophia Lopes Ribeiro Fiorotto, 2023 (jointly supervised with Luciana Basualdo Bonatto). Braid, knots and links
• Sebastián Camilo Daza Alfonso, 2021. G‑structures on orbifolds
• Marcelo Barbosa Viana, 2018. Finite simplicial complexes and Euler’s theorem
• Gustavo Ignácio Duarte, 2018. Spencer cohomology and the integrability of G‑structures
• Luciana Basualdo Bonatto, 2017. The Bott periodicity theorem from an algebraic topology viewpoint

Visitors

Four of us in the Department of Mathematics of IME-USP work on Poisson geometry and related topics: Clarice Netto, Cristian Ortiz, Fabricio Valencia and me. With our students and postdocs, it is an exciting place to work.

Visitors are very welcome. If you would like to visit me and my students, for a few days or for a longer stay, please write to me.

Visitors I have received include:

• Francesco Cattafi (Würzburg), February–April 2026
• Luciana Basualdo Bonatto (Oxford), every year since 2025
• Wilmer Smilde, 2025
• David Martínez Torres, April–June 2023
• Rui Loja Fernandes (University of Illinois), regularly
• Ioan Mărcuţ, 2014
• Daniele Sepe, 2013
• Maria Amelia Salazar, 2013
• João Nuno Mestre
• Florian Zeiser
• Joel Villatoro