The study of the filamentary Cosmic Web is a paramount aspect of modern research in cosmology. With the advent of extremely large and precise cosmological datasets which are now (or within months) coming notably from the Euclid space mission, it becomes feasible to study in detail the formation of cosmic structures through gravitational instability. In particular, fine non-linear aspects of this dynamics can be studied from a theoretical point of view with the hope of detecting signatures in real observations. One of the major difficulty in this regard is probably to make the link between the observed distribution of galaxies along filaments and the underlying matter distribution for which first-principles models are known. Building on recent and state of the art theoretical developments in gravitational perturbation theory and constrained random field theory, the successful candidate will develop first-principles predictions for statistical observables (extrema counts, topological estimators, extrema correlation functions, e.g. Pogosyan et al. 2009, MNRAS 396 or Ayçoberry, Barthelemy, Codis 2024, A&A 686) of the cosmic web, applied to the actual discrete field of galaxies which only traces the total matter in a biased manner. This model will then be applied to the analysis of Euclid data.