Modern diagrammatic many body techniques.

In this talk I will discuss recent progress on the development of unbiased diagrammatic techniques for strongly-correlated many-body systems. The formalism we have developed allows to elegantly and efficiently encode the fundamental structure of quantum-many theory using renormalized expansions as the building block. Within this framework it is easy to incorporate, for instance, well-established many-body approximations like Dynamical Mean Field Theory as the starting point of a pertubative expansion. In particular, I will present state-of-the-art results in two and three dimensional Fermi-Hubbard models away from half filling in the non-perturbative regime.