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Low dissipation, strongly interacting material systems are an exciting frontier in condensed matter physics and materials science. These systems order in exotic and unpredictable ways, exhibiting emergent ordering that is fundamentally challenging understand and potentially extremely useful for next generation materials. My group is focused upon creating new materials composed of photons or photonic quasi-particles. I will present recent work demonstrating that braiding of 2D transmission lines leads to knotted photonic band-structures, corresponding to time-reversal-invariant topological insulators. I will further describe progress in ongoing efforts to develop materials consisting cavity Rydberg polaritons, whose strong, coherent interactions have the potential to study crystallization and other traditionally soft-matter phenomena in a quantum regime.