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Explore the behavior of shear-oscillated amorphous materials in this 32-minute conference talk from the Thematic Programme on "Non-equilibrium Processes in Physics and Biology" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into a study using a simplified, coarse-grained model to characterize material responses to oscillations. Examine how poorly annealed and ultra-stabilized materials react differently to small oscillations, and discover the critical threshold that triggers a sudden, discontinuous transition to a mixed state with a fluid shear-band within a marginally stable solid matrix. Investigate the quantitative relationships between uniform shear and steady-state conditions, and analyze the transient phase involving shear band development and movement. Gain insights into the evolution of amorphous solids under various shear-oscillation conditions and their implications for material science and physics.