My research is mainly focused on the interaction between real algebraic geometry and geometric measure theory. 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 aspects of Riemannian and sub-Riemannian geometry on 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)
J. Eur. Math. Soc. (JEMS) (accepted)
My PhD thesis "Sard properties for polynomial maps in infinite dimension and applications to sub-Riemannian geometry" is available at the following link.
RESEARCH GROUPS
STARS Starting Grant 2023 - NewFrac