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Explore time-driven wave systems and out-of-equilibrium dynamics in this 53-minute conference talk that examines material and electromagnetic resonances structured in both space and time. Discover how time serves as a degree of freedom to manipulate frequency and momentum response while enabling non-reciprocal and amplification regimes. Learn about recent research results combining strong tailored nonlinearities in metasurfaces with driven systems, creating new opportunities for photonic engineering. Investigate exotic phenomena including time reflections, momentum bandgaps, synthetic rotations, and Penrose super-radiance for photons. Examine the unique light-matter interactions arising in these systems and understand their potential applications for advancing wave physics and photonic technologies through Floquet metasurface implementations.