These notes are an extended version of a talk given by the author in the
seminar "Theorie Spectrale et Geometrie" at the Institut Fourier in No- vember
2016. We present here some aspects of a work in collaboration with B. Collier
and N. Tholozan (arXiv:1702.08799). We describe how Higgs bundle theory and
pseudo-hyperbolic geometry interfere in the study of maximal representations
into Hermitian Lie groups of rank 2
