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On passe en revue une approche unifiee aux conjectures de Manin-Mumford et d'Andre-Oort basee sur la combinaison de techniques galoisiennes et ergodiques. Ce texte est base sur les travaux recents de Klingler, Ullmo et Yafaev sur la conjecture de Andre-Oort, et de Ratazzi et Ullmo sur la conjecture de Manin-Mumford.

Galois orbits and equidistribution: Manin-Mumford and André-Oort.