Superconductivity beyond Migdal's theorem and the role of density of states singularities

The breakdown of Migdal's theorem requires the modification of the electron-phonon theory of superconductivity in order to include the nonadiabatic contributions. The novel features arising from this scenario are relevant for both the fullerene compounds and the oxides. In particular, the interplay between the nonadiabatic contributions and the van Hove singularities in the cuprates provides a simple explanation for the highest values of T-c found in these materials. We also discuss the possible role of other type of peaks in the density of states like those that could be induced by stripes.