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Systems with long-range interactions present paradoxes by comparison with usual statistical mechanics results. One might encounter negative specific heat, inequivalence of the microcanonical and canonical ensembles, temperature jumps... We will present several recent theoretical advances to explain the statistical mechanics and the dynamical features of such systems. We will consider not only toy models but also several application domains (astrophysics, 2D hydrodynamics, spin chains,...). Host: Philippe Odier |