Abstract: An accurate description of short-range physics is one of the main challenges in the study of strongly interacting many-body quantum systems. In nuclear systems, short-range correlations (SRCs) have been studied extensively in the last decades using both large momentum transfer quasi-elastic reactions and ab-initio calculations.

In this talk, I will present an overview of the Generalized Contact Formalism, an effective model based on the short-range factorization of the many-body wave function, that allows to obtain a comprehensive picture of the effects of SRCs in nuclei. I will then discuss recent results in which first signature of three-nucleon correlations is observed, as well as application for the calculation of neutrinoless double beta decay matrix elements. Finally, I will present an extension of the formalism which includes sub-leading corrections to the wave-function factorization, towards a systematic short-range expansion of the nuclear many-body problem.