Heavy-flavour observables within a (3+1)D transport approach

In this contribution we display our first predictions for heavy-flavour observables in heavy-ion collisions obtained extending our well-established POWLANG transport setup to perform full (3+1)D simulations. In particular, we show our findings for the directed-flow coefficient $v_1$ and for the nuclear modification factor $R_{\rm AA}$ and elliptic-flow $v_2$ at forward rapidity: in both cases one needs to drop the approximation of longitudinal boost-invariance, usually enforced in most numerical implementations of the transport equations and assumed in our past publications. We briefly discuss how from a theory-to-data comparison one can get a richer (3+1)D information on the initial geometry of the fireball and put tighter constraints on the heavy-flavour transport coefficients.