Mathematics

 There is growing amount of experimental, numerical, and theoretical evidence that, in the presence of sufficiently strong quenched disorder, interacting quantum particles are many-body localised: transport is suppressed and memory of the initial condition is preserved locally for arbitrarily long times. A theoretical understanding of the many-body localised phase has recently emerged in terms of approximately local, conserved operators. In this talk, I will recall some basic features of localised systems in the single-particle setting, and discuss in which sense the notion of localisation can be extended to interacting systems by means of the conserved quantities. I will discuss how conserved operators can be constructed for a particular model of interacting fermions on the lattice, and briefly comment on the implications for ergodicity and thermalisation.