Slow dynamics and non-ergodicity due to kinetic constraints, from classical to quantum

Classical many-body systems that display slow collective relaxation - the canonical example being those that form glass - do so due to effective constraints in the their  dynamics. The simplest manifestation of this principle is  in kinetically constrained models (KCMs) where dynamical constraints are explicit. After reviewing the basic properties of constrained dynamics, I will discuss how similar ideas can be made relevant for quantum many-body. I will describe quantum KCMs which display slow thermalisation, and in certain cases non-ergodicity, in the absence of disorder, with focus on the "quantum East model" as a concrete example. I will discuss connections with related problems such as quantum scars and fractons. My main aim will be to highlight links between concepts and methods of classical and quantum non-equilibrium.