Filippo Bracci is currently mainly working on geometric function theory in several complex variables and local dynamics of germs of holomorphic diffeomorphisms. More in details, one of the main theme is the interplay between Andersen-Lempert approximation theory and embedding of univalent maps into normal Loewner chains in higher dimension. Another related subject of his research is the study of the compact class of univalent maps admitting parametric representation, the so called class S^0, especially with the aim of finding support points and studying a Bieberbach type conjecture in higher dimension. Also, in order to study boundary behavior of univalent maps on hyperbolic domains (or more general on complete Kobayashi hyperbolic manifolds), he is working on a generalization of Carathéodory prime ends theory via intrinsic metric, and the various questions which this construction raises up, such as, for instance, the relations of the newly defined boundary with Gromov's boundary and Busemann boundary. Regarding local dynamics of holomorphic diffeomorphisms, Bracci is interested in the question of existence of parabolic curves for germs of biholomorphisms fixing the origin and tangent to the identity in the complex three-dimensional space. Also, his interest is in studying the different global basins of attraction which might appear as extension of local basins of attraction of automorphisms.