# Event № 959

*Abstract:*

Under certain congruence conditions, the elliptic curves defined over the complex numbers with complex multiplication (CM) by a given order can be reduced to supersingular curves (SSC) defined over a finite field of prime characteristic. The (finite) set of isomorphism classes of SSC curves carries a natural probability measure. It was shown by Philippe Michel via progress on the subconvexity problem that the reductions of CM curves equidistribute among the SSC curves when the discriminant of the order diverges along the congruence conditions. We will describe a proof of equidistribution in the product of the simultaneous reductions with respect to several distinct primes of CM curves of a given order using a recent classification of joinings for certain diagonalizable actions by Einsiedler and Lindenstrauss. This is joint work with Menny Aka, Philippe Michel, and Andreas Wieser.