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Abstract : Different notions of complexity have been argued to be relevant in black hole physics, holography and, more broadly, in many body long time physics. In this talk, after reviewing the notion of spread complexity and its main features, we shall discuss its relation to the momentum of an infalling particle in AdS/CFT, how to quantify its sensitivity with the change of initial state and, time permitting, how to use this observable to explore the breakdown of effective field theories at long time scales, as in holography within large N limits.