Research

My research interests are focused on topics from Differential Geometry/Topology, Symplectic Geometry/Topology, Lie Theory and Mathematical Physics. I've worked with invariant geometric objects on Lie groups as well as homogeneous spaces. I'm also interested in studying more general structures as for instance Lie groupoids, Lie algebroids and differentiable stacks. You may find below my preprints and publications.

arXiv                                                 Google Scholar                                                            Mathscinet                                                                     ORCID

Preprints

1. Hamiltonian actions on 0-shifted cosymplectic groupoids, (2025), 1-11.  See arXiv. (With D. López-Garcia).

2. Topology of singular foliations of closed 1-forms on orbifolds, (2025), 1-21. See arXiv. (With D. López-Garcia).

3. Lecture notes on the symplectic geometry of graded manifolds and higher Lie groupoids, (2025), 1-88. See arXiv. (With M. Cueca and A. Maglio).

4. Basic sections of LA-groupoids. Available upon request. (With A. Maglio).

Papers

1. Novikov type inequalities for orbifolds, Mathematische Annalen 392 (2025) no. 4, 4543 - 4572. See arXiv or published. A recorded talk (in Spanish), motivating the classical problem is here.

2. On the monodromy action for f(x,y)=g(x)+h(y), Proceedings of the American Mathematical Society 153  (2025) No. 5, 1881–1892. See arXiv or published. (With D. López-Garcia).

3. Double extension of flat pseudo-Riemannian F-Lie algebras, Journal of Algebra 666 (2025), 1-27. See arXiv or published. (With A. Torres-Gomez).

4. Morse theory on Lie groupoids, Mathematische Zeitschrift 307 (2024) 46: 1-55. See arXiv or published. (With C. Ortiz).

5. Isometric Lie 2-group actions on Riemannian groupoids, The Journal of Geometric Analysis  323 (2023) 33: 1-36. See arXiv or published  (With J. S. Herrera-Carmona).

6. Invariant generalized almost complex structures on real flag manifolds, The Journal of Geometric Analysis, 296 (2022) 32: 1-40. See arXiv or published. (With C. Varea).

7. Left invariant special Kähler structures, Indagationes Mathematicae, 33 (2022) No. 3, 598–624.  See arXiv or published.

8. Invariant Generalized Complex Geometry on Maximal Flag Manifolds and Their Moduli, Journal of Geometry and Physics 163 (2021), 104108. See arXiv or published. (With E. Gasparim and C. Varea).

9.  Infinitesimally tight Lagrangian orbits, Mathematische Zeitschrift, 297 (2021) No. 3, 1877-1898. See arXiv or published. (With E. Gasparim and L. A. B. San Martin).

10.  Flat affine symplectic Lie groups, Journal of Lie Theory 31 (2021), No. 1, 063-092. See arXiv or published. 

11.  Lecture notes on quivers with superpotential and their representations, São Paulo Journal of Mathematical Sciences 15 (2021), 720-743. See published. (With A. Quintero-Vélez).

12.  Notes on flat pseudo-Riemannian manifolds, Pro Mathematica 30 (60), (2019) 11-50. See arXiv or published.

PhD thesis: Morse theory on Lie groupoids. Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil, (2024).