Research Focus
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).
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.