In project W01, we will address fundamental questions of topological features in quantum systems and photonics for strongly driven, interacting many-particle systems, as they occur in intense laser-matter interactions, for instance.  With our combined theoretical and experimental efforts we will answer how topological invariants can be properly defined in nonlinear systems, and what the shapes and characteristics of topological edge states in interacting or nonlinear systems are. Further, we will investigate how topological invariants and the associated topological features behave under dimensional mapping. With our findings we will pave the way to experimentally explore multi-electron dynamics using a photonic platform.