I will discuss ongoing work in my group to develop strongly interacting photons as a platform for exploring few- to many- body physics. We have recently demonstrated that non-planar optical resonators may be employed to investigate quantum Hall physics in curved space, and I will discuss our progress towards the strongly-correlated regime via photon-photon interactions mediated by Rydberg excitations, as well as response to curvature as a measure of quantized transport coefficients. I will also describe the development of Chern-insulating microwave circuits compatible with transmon-mediated interactions. A looming challenge is the population of topological groundstates in synthetic systems. To this end, I will conclude with a description of our plans for both particle-by-particle construction- and dissipative stabilization- of Laughlin states.