Stellar clusters are ubiquitous in all luminous galaxies and can be used as tracers of galaxy formation and evolution if we understand their growth and assembly into their host systems. To this end, issues yet open in our understanding of these objects need to be investigated. Stellar population (SP) models have yet to properly predict properties of globular clusters (GCs) outside our Galaxy, such as colours and chemical abundances. GC colour-metallicity relations have long been a topic of debate in the literature, with recent evidence suggesting a non-linear structure. Moreover, the environment influence in nuclear star cluster occupation statistics is not completely understood, despite providing important clues to the galaxy mass assembly in clusters/groups. In this context, our goal is threefold: We will use near-infrared (NIR) spectra of GCs in the galaxy NGC~5128, as well as public available optical data, to test age and metallicity predictions of SP models. Furthermore, we will implement the mixture of copulas technique to identify GC subpopulations and properly model the proposed non-linear structure of colour-metallicity relations in the rich system of the M87 galaxy. Finally, we will study galaxy nucleation in the extreme environment of the largest mass concentration of the nearby universe, the Shapley Supercluster, using deep HST data and a hierarchical Bayesian framework. Ahead of the imminent dawn of the next generation of telescopes which will provide unprecedented amounts of extragalactic stellar cluster data, this project aims at investigating three of the most important open questions in the field, as well as providing publicly available resources to the community. This will be in the form of reduced NIR GC spectra to aid in SP studies and open-source software to streamline the implementation of mixture of copulas to extragalactic GC datasets.
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