Abstract
Advances in the self-consistent Green's function approach to finite nuclei are discussed, including the implementation of three-nucleon forces and the extension to the Gorkov formalism. We report results on binding energies in the nitrogen and fluorine isotopic chains, as well as first ab-initio calculations for medium-mass open-shell chains ranging from argon to titanium. Results with chiral interactions put in evidence the important role played by 3NF in neutron rich isotopes.