Research

My research is in the field of Complex Differential Geometry. I am interested in studying special structures on smooth manifolds, with particular attention to complex and almost complex structures, symplectic and almost symplectic structures, generalized complex structures and SU(m)-structures
Among the techniques I use, it is worth mentioning: homological algebra and spectral sequences, cohomologies of complex or symplectic differential operators, deformations of structures, Hodge theory and spaces of harmonic forms, existence of special metrics. My theoretical results are always complemented by a large number of examples, most of them regarding invariant structures on homogeneous manifolds.

My current projects are focused on several aspects of complex or almost complex manifolds, and of SU(m)-structures. More precisely, there are two geometrical objects that encode several information for those structures: the Nijenhuis tensor and the canonical bundle. For the former, I am studying the distribution provided by its image on low-dimensional manifolds. For the latter, I am exploring the connection between SU(m)-structures and the Kodaira dimension of almost complex manifolds, recently defined by Chen and Zhang. I also study small deformations and the moduli space of those structures under constraints for their intrinsic torsion.

During my PhD, I focused on the study of invariants of almost complex and almost symplectic manifolds. The main goals were defining new invariants for those structures and studying the already existing ones. The results obtained led to a defnition of Bott-Chern and Aeppli cohomologies of almost complex and almost symplectic manifolds and to the study of spaces of harmonic forms built using almost complex and almost symplectic operators on almost Hermitian manifolds. The theory developed in the non-integrable cases has interesting applications also to the integrable cases, in particular on complex surfaces.

Check out my publications for more details!