| Résume | I'll discuss some joint work with Binyamini, Schmidt, and Thomas, in which we prove an effective and uniform version of Manin-Mumford for products of CM elliptic curves. I'll show how we deduce from this an effective Andre-Oort result for fibre powers of the Legendre family. I'll then discuss some work in progress with Schmidt , on extending the above to multiplicative extensions, and perhaps some other similar results. |