Research

My main research interests lie in differential geometry, more precisely in the interplay between Lie groupoids and geometric structures, including G-structures, Cartan geometries and foliations. I also draw inspiration, tools and ideas from Poisson geometry and the theory of PDEs on jet bundles.

See also my profiles on arXiv, Orcid, Google Scholar, MathSciNet and Zentralblatt MATH.

My Erdős number is 5, but my Erdős-Bacon number is still infinite. You can find my mathematical family here (notable relatives: my (great^10)-grandfather is Leonhard Euler and my (great^14)-one is Gottfried Leibniz).

My research statement is available upon request.

Forthcoming research book

📕 Pseudogroups and geometric structures (with L. Accornero, M. Crainic and M.A. Salazar), ~400 pages (available on request)

Research papers

📰 PB-groupoids vs VB-groupoids, Revista Matemática Iberoamericana (with A. Garmendia)

DOI: 10.4171/rmi/1580, arXiv: 2406.06259

📰 Cartan geometries and multiplicative forms, Differential Geometry and its Applications 75C (2021) 101722

DOI: 10.1016/j.difgeo.2021.101722, arXiv: 1911.13147

📰 From PDEs to Pfaffian fibrations, L'Enseignement Mathématique 66 (2020), 187-250 (with M. Crainic and M. Salazar)

DOI: 10.4171/LEM/66-1/2-10, arXiv: 1901.02084

📰 Variational derivatives in locally Lagrangian field theories and Noether-Bessel-Hagen currents, International Journal of Geometric Methods in Modern Physics, 13(8), 1650067 (2016) (with M. Palese and E. Winterroth)

DOI: 10.1142/S0219887816500675, arXiv: 1601.07193

Preprints

📄 A groupoid approach to transitive differential geometry, arXiv:2211.16639 (with L. Accornero)

📄 Pseudogroups of symmetries and Morita equivalences, arXiv:2211.01319 (with L. Accornero)

Expository papers

📄 Diffeology, WikiJournal Preprints, currently under public peer-review (with D. Miyamoto)

📰 Poisson manifold, WikiJournal of Science 7(1): 6, 2024

DOI: 10.15347/wjs/2024.006, Wikidata Q117054291, ISSN 2470-6345

Papers in progress

📝 "Non-transitive" Cartan geometries associated to contact subriemannian structures (with I. Beschastnyi, A. Čap and J. Mestre)

📝 Multiplicative Haefliger foliations (with M. Jotz)

Lecture notes

📒 Geometric mechanics (2025), 95 pages (available on request)

📒 Introduction to topology (2025), 86 pages (available on request)

📒 Lie groupoids and Poisson geometry (2024), 73 pages (available on request)

Theses

📔 PhD Thesis: A general approach on almost structures in geometry (supervised by Marius Crainic, defended on 26 February 2020)

ISBN 978-90-393-7257-9, available also on the Utrecht University repository 

📔 Master Thesis: Conservation Laws in Variational Sequences (supervised by Marcella Palese, defended on 17 July 2015)

📔 Bachelor thesis: Characteristic curves for PDEs: theory and application to Klein-Gordon equation in metric-affine formalism (supervised by Lorenzo Fatibene, defended on 18 July 2013)