I will show that manifolds with positive Ricci curvature have infinitely many minimal smooth embedded hypersurfaces. This is joint work with Fernando Marques

Rademacher theorem states that every Lipschitz function on the Euclidean space is differentiable almost everywhere, with respect to the Lebesgue measure. I will discuss an extension of this theorem where the Lebesgue measure is replaced by an arbitrary measure. Time permitting, in the last part of the talk, I will show some applications of this result about the theory of currents. This is joint work with Giovanni Alberti.