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Can time-translation invariance be spontaneously broken? The possible existence of time-crystals was first addressed by Wilczek for quantum many-body systems launching an intense activity both theoretically and experimentally. Despite their conceptual simplicity and apparent similarity to ordinary crystals, they were experimentally observed only a few years ago, eighty years after the Landau theory of symmetry breaking.
I will give an overview of the field focusing on the most recent theoretical and experimental advances.