The relative dendroidal Rezk nerve and (some of) its applications

It is a classical, but quite beautiful and useful, result that (derived) localization, i.e. the process of inverting morphisms in a homotopy-coherent way, establishes an equivalence of homotopy theories between that of infinity-categories and that of ordinary categories equipped with a collection of (wanna-be) equivalences, aka relative categories. In recent times, this has been extended to relative (infinity-)operads thanks to Pratali's operadic generalization of Joyal's delocalization theorem. Despite the fact that this has interesting theoretical applications, e.g. it was exploited to address an open question posed by Harpaz regarding the comparison of simplicial operads and Lurie quasioperads, it is a difficult task to explicitly compute localizations of relative categories/operads in practice. In this talk, we will be concerned with a handy explicit model for these derived localizations of (infinity-)operads called the relative dendroidal Rezk nerve, which is the obvious operadic generalization of a well-known construction due to Rezk in the categorical setting, and some computations performed using this model. Based on joint work with K.Arakawa and F.Pratali, arXiv:2606.11895 and arXiv:2512.16374.