The goal of this thesis is to understand the individual and combined impact of non-reciprocal interactions and activity in collective phenomena emerging when density is high keeping in mind real-world systems like dense human crowds. Building on our existing understanding of active systems, the first objective is to confirm or rule out the emergence of comparable behaviour from non-reciprocity. This requires the identification of appropriate models and the targeted exploration of well-chosen parameter ranges. The goal is then to combine non-reciprocity with activity to quantify the possible impact when non-reciprocity is ignored in active models. While keeping the focus on comparison with real-world systems, fundamental questions will be natural stepping stones as for example on the existence of phase transitions in one dimension and two dimensions (equilibrium theorems do not apply). The project will take place at Gulliver (ESPCI UMR 7083 CNRS) and be supervised by L. Berthier (DR, CNRS). The lab has developed well-known expertise for the study of disordered and non-equilibrium materials, and has a large experience regarding the numerical simulations of these systems [4]. The work will also be performed in close collaboration with J. Klamser (L2C, CNRS, Montpellier).