In '78, M. Kashiwara and M. Vergne had conjectured in one of their papers that the Baker-Campbell-Hausdorff's series, for a real Lie algebra $\mathfrak g$, solves two universal equations concerning power series valued in the free Lie algebra generated by two indeterminates. This property implies the Duflo's isomorphism between the center of the universal enveloping algebra of $\mathfrak g$ an the Poisson center of the symmetric algebra of $\mathfrak g$. The Kashiwara-Vergne's conjecture has been completely solved by A. Alekseev et E. Meinrenken in 2005. The proof uses the Kontsevich's quantization.