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. Currently, I'm interested in studying more general structures as for instance Lie groupoids, Lie algebroids and differentiable stacks. You may find below my preprints, publications, and work in progress. 

arXiv                                                 Google Scholar                                                            Mathscinet                                                                     ORCID

Preprints

1. Double extension of flat pseudo-Riemannian F-Lie algebras, submitted for publication (2024). See arXiv. (With A. Torres-Gomez).

2. On the monodromy action for f(x,y)=g(x)+h(y), submitted for publication (2023). See arXiv. (With D. López-Garcia).

3. Novikov type inequalities for orbifolds, submitted for publication (2023). See arXiv. A recorded talk (in Spanish), motivating the classical problem is here.

Papers

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

2. 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)

3. 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).

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

5. 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).

6.  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).

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

8.  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).

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

Work in progress

1. Closed geodesics on Riemannian stacks (With C. Ortiz and L. Vitagliano).

2. Reduction of 0-shifted contact structures (With A. Maglio).

3. Morse theory for Lie n-groupoids.

4. Affine representations of Lie groupoids and their Lie algebroids (With D. Lopez-Garcia and N. Martinez-Alba).