  Let U:=L\G be a homogeneous variety defined over a number field K, where G is
a connected semisimple K-group and L is a connected maximal semisimple
K-subgroup of G with finite index in its normalizer.
  Assuming that G(K_v) acts transitively on U(K_v) for almost all places v of
K, we obtain the asymptotic of the number of rational points in U(K) with
height bounded by T, and settle new cases of Manin's conjecture for many
wonderful varieties. The main ingredient of our approach is the
equidistribution of semisimple adelic periods, which is established using the
theory of unipotent flows.
