Dynamics in mean-field spin-glasses

The anomalous dynamical properties of out-of-equilibrium glassy systems, like an extremely slow relaxation to equilibrium, long-time memory effects or aging, have been studied by physicists since 1970's. However the rigorous understanding of these properties is still rather unsatisfactory. In my talk I will summarise the recent advances in this field: First, some older results obtained for the so-called trap-model dynamics in the Random Energy model, and then a new result on the dynamics of p-spin spin glasses.