The Functional Renormalisation Group: From the physics of strongly correlated systems to generative models

In the past decades, the functional renormalisation group (fRG) has matured into a comprehensive approach to strongly-correlated (non-perturbative) systems, covering quantitatively both universal and non-universal phenomena. The fRG also constitutes an ideal approach for unravelling structural aspects of quantum field theories. This is not only interesting for studies in mathematical physics, but also guides systematic diagrammatic expansion schemes. It is also used to set up novel statistical (lattice) approaches to non-perturbative phenomena. In the present talk I survey these advances and illustrate the progress with selected examples ranging from ultracold atoms, QCD and quantum gravity to novel generative architectures for lattice simulations and beyond.