Strongly correlated fermions are ubiquitous in various contexts: electrons in solids or molecules, nucleons in nuclei or neutron stars, quarks in QCD. Our understanding of such systems is limited by the difficulty to compute their properties in a reliable and unbiased way. For conventional quantum Monte Carlo methods, the computational time generically grows exponentially with the number of fermions (due to the “fermion sign problem”). The situation is fundamentally different with connected Feynman diagrams, which can be computed directly for infinite volume. In contrast to usual diagrammatic calculations, we control the series-truncation error by going to high orders. To this end we develop Monte Carlo algorithms to efficiently sample diagrammatic series. In the cases where the series diverges, we study its the large-order asymptotic behavior, and use it to construct a resummation method capable of transforming the divergent series into a result that converges towards the exact physical value (in the limit of infinite truncation-order). The internship/PhD project involves the development of diagrammatic Monte Carlo for the unitary Fermi gas model and/or impurity models (that accurately describe experiments on ultracold atomic gases conducted in several labs, e.g. LKB, MIT, Hamburg, Technion, Yale…).