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Ab-initio predictions of nuclei with masses up to A~100 or more is becomingpossible thanks to novel advances in computations and in the formalism ofmany-body physics. Some of the most fundamental issues include how to deal withmany-nucleon interactions, how to calculate degenerate--open shell--systems,and pursuing ab-initio approaches to reaction theory. Self-consistent Green'sfunction (SCGF) theory is a natural approach to address these challenges. Itsformalism has recently been extended to three- and many-body interactions andreformulated within the Gorkov framework to reach semi-magic open shellisotopes. These exciting developments, together with the predictive power ofchiral nuclear Hamiltonians, are opening the path to understanding largeportions of the nuclear chart, especially within the $sd$ and $pf$ shells. Thepresent talk reviews the most recent advances in ab-initio nuclear structureand many-body theory that have been possible through the SCGF approach.

Many-body Propagator Theory with Three-Body Interactions: a Path to Exotic Open Shell Isotopes