  We study attractor points for Calabi-Yau variations of Hodge structures. In
particular, for certain moduli spaces which are Shimura varieties, we prove
that the attractor points are CM points, thus proving Moore's Attractor
Conjecture in these cases. We also study non-BPS examples of attractors,
obtaining special points on locally symmetric spaces without hermitian
structures, as well as locally symmetric spaces inside Shimura varieties; for
the latter we point out a possible analogy with subspaces studied by
Goresky-Tai. Finally we give an explicit geometric description of non-BPS
attractors in the simplest case.
