My research is in the field of Complex and Differential Geometry. I am interested in studying special structures on smooth manifolds, with particular attention to Complex/Almost Complex Structures, Symplectic/Almost Symplectic Structures and Generalized Complex Structures.
Among the techniques I use, it is worth mentioning: Homological Algebra and Spectral Sequences, Cohomologies of complex/symplectic differential operators, deformations of structures, Hodge theory and spaces of harmonic forms, existence of special metrics.
My PhD project focuses on the study of invariants of almost complex and almost symplectic manifolds. Its main goals are defining new invariants for those structures and studying the already existing ones. The results obtained so far led to a defnition of Bott-Chern and Aeppli cohomologies of almost complex 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. Our theoretical results are always complemented by a large number of examples, most of them regarding invariant structures on homogeneous manifolds.
Check out my publications for more details!