Giovanni Alberti (born March 21, 1965) is an Italian mathematician who is active in the fields of calculus of variations, real analysis and geometric measure theory.

Alberti has studied at Scuola Normale Superiore under the guide of Giuseppe Buttazzo and Ennio De Giorgi; he is professor of mathematics at the University of Pisa.

Alberti is mostly known for two remarkable theorems he proved at the beginning of his career, that eventually found applications in various branches of modern mathematical analysis.

[1] The second asserts the rank-one property of the distributional derivatives of functions with bounded variation, thereby verifying a conjecture of De Giorgi.

[2] This theorem has found several applications, as for instance in the Ambrosio's proof of an open problem posed by Di Perna and Lions concerning the well-posedness of the continuity equation involving BV vector fields.