On the geometry of some special subvarieties contained in the Torelli locus
Almost all the examples of special (or Shimura) subvarieties of A_g contained in the Torelli locus are given by families of Jacobians of Galois covers of the projective line or of elliptic curves. They satisfy a sufficient condition that I will explain. This condition is also necessary in the case of double covers of elliptic curves. I will discuss the geometry of some examples of Galois covers of elliptic curves yielding special subvarieties of A_3, which are fibered in totally geodesic curves and hence contain countably many Shimura curves.