[4][5] She earned a laurea in mathematics in 2014, at the University of Turin, and a laurea magistrale in 2016, at the University of Milano-Bicocca, the Italian equivalents of a bachelor's and master's degree, mentored by Susanna Terracini and Veronica Felli respectively.

[2] She completed her doctorate (DPhil) at the University of Oxford in England in 2020, with the dissertation Vectorial problems: sharp Lipschitz bounds and borderline regularity supervised by Jan Kristensen.

[2] De Filippis' research is mainly devoted to problems from regularity theory in elliptic and parabolic partial differential equations, with special emphasis on those coming from the Calculus of Variations.

Together with Giuseppe Mingione, she proved a Schauder type theory for nonuniformly elliptic equations and functionals.

[1][7][8] She made extensive use of nonlinear potential theoretic methods in the context of elliptic regularity.