Research Focus
Differential Geometry
I study geometric structures in the spirit of Lie and Cartan, using techniques from Lie theory. In particular, I use algebroids and their integrations to classify global solutions to geometric problems. Typically, the geometric problem consists of a structure (e.g. a Riemannian metric) subject to a diffeomorphism-invariant equation. These problems sit at the intersection of Lie integration theory and partial differential equations, and I am developing the framework of relative algebroids to bridge the two.
Publications
1. Notes on relative algebroids. arXiv:2510.21987 (2025). To appear in INdAM.
2. Relative algebroids and symmetries of Pfaffian fibrations. arXiv:2510.01517 (2025).
3. Relative algebroids and Cartan realization problems (with Rui Loja Fernandes). arXiv:2503.19233 (2025). Accepted for publication in Selecta Mathematica.
4. Lie groups of Poisson diffeomorphisms. Journal of Symplectic Geometry 21 (2023), no. 5, 889–937.
5. Linearization of Poisson groupoids. Indagationes Mathematicae 33 (2022), no. 3, 682–717.