  This is the English translation of a short note published by Gazette des
Math\'ematiciens. The author was asked to present the recent work of Alex Eskin
and of Maryam Mirzakhani, arXiv:1302.3320, and their joint work with Amir
Mohammadi, arXiv:1305.3015, on SL(2,R)-action on the moduli space of Abelian
differentials. This is a popularization paper with no proofs. Its only purpose
is to suggest some motivations, and to outline possible applications
considering billiards in polygons as an example.
