Ergodicity breaking in quantum dynamics

When can isolated many body quantum systems fail to go to equilibrium under their own dynamics, and how robust can this 'ergodicity breaking’ be? This question has been a central theme of research in quantum dynamics and statistical mechanics over the past decade, and I will share with you some highlights, focusing on three key developments: many body localization, dynamics with multipolar symmetries, and dynamics with higher form symmetries. I will present the rich and exotic phenomena that arise in these three regimes, and how they may be realized experimentally. I will then discuss some key open directions for the field.