Scale hierarchies are a cornerstone of our understanding of the natural world. They come particularly into play in the study and minimisation of scalar potentials, whose importance in particle physics became obvious with the Higgs boson discovery. Yet, as was realised quickly during the construction of the Standard Model of particle physics (SM), quantum scalar potentials are quite adverse to involving more than one given scale at the time. Within the SM, this led to the (in)famous hierarchy problem and to the theoretical search for mechanisms protecting the electroweak (EW) scale. We have found recently that scalar‑field potentials can be organised using “maximally‑symmetric” structures via moment‑map techniques, forming an ordered tree of increasingly symmetric operators. This systematic ordering naturally generates light scalars. The internship can focus on two possible directions. First, promising results in solving the little hierarchy problem have been obtained in a simple model of an extended Higgs sector. A thorough study of the existing constraints and prediction for the electroweak precision observables must be undertaken. Second, since the mechanism only generates scale hierarchies of about one to two orders of magnitude, a key question is whether it can be linked to another solution for the full hierarchy problem. Models with extra-dimensions will be an interesting starting point.