My research activity is focused on the interaction between real algebraic geometry and smooth analysis. In particular, I am interested in Sard-type theorems for maps defined on infinite dimensional spaces and in their applications to sub-Riemannian geometry.
I am also interested in some aspects of Riemannian geometry in infinite dimensional manifolds.
A remark on vanishing geodesic distances in infinite dimensions. (with V. Magnani)
Proc. Amer. Math. Soc. (2020)
Rev. Mat. Complut. (2022)
The Michor-Mumford conjecture in Hilbertian H-type groups. (with V. Magnani)
J. Geom. Anal. (2025)
Quantitative approximate definable choices. (with A. Lerario and L. Rizzi)
Math. Ann. (2025)
Sard properties for polynomial maps in infinite dimension. (with A. Lerario and L. Rizzi)
arxiv preprint (2024), submitted
My PhD thesis "Sard properties for polynomial maps in infinite dimension and applications to sub-Riemannian geometry" is available at the following link.