Representations of quasi-projective fundamental groups and the structure of transversely projective foliations

Corlette and Simpson classified Zariski dense rank-two representations of fundamental groups of quasi-projective manifolds under the aditional assumption that the monodromy is quasi-unipotent at infinity. I will explain how to avoid such extra assumption, and how to obtain a similar classification for singular transversely projective foliations on projective manifolds.