Galois orbits and equidistribution: Manin-Mumford and André-Oort (Q1032658)

In this review article, the author outlines a similar proof of the Manin-Mumford conjecture and the André-Oort conjecture. This proof is based on a ``Galois theory -- ergodic theory alternative''. In the case of the Manin-Mumford conjecture, it is due to \textit{N. Ratazzi} and \textit{E. Ullmo} [``Galois + equidistribution = Manin-Mumford'', Clay Math. Proc. 8, 419--430 (2009; Zbl 1250.11062)] and in the case of the André-Oort conjecture, it is due to B. Klingler, E. Ullmo and A. Yafaev [``On the André-Oort conjecture for products of modular curves.'', Clay Math. Proc. 8, 431--439 (2009; Zbl 1254.11062); B. Klingler and A. Yafaev, ``Galois orbits and equidistribution of special subvarieties: towards the André-Oort conjecture'', preprint \url{http:www.institut.math.jussieu.fr/~klingler/papiers/KY12.pdf}].