Exploring Flatland with cold atoms

The physics of many-body systems strongly depends on their dimensionality. For example, in a two-dimensional world, most standard phase transitions towards an ordered state of matter like crystals or magnets would not occur because of the increased role of fluctuations. However, non-conventional phase transitions can still take place, as understood by Kosterlitz and Thouless (2016 Nobel prize). In this talk I will present some important features of Flatland physics explored with cold atomic gases, such as the existence of a superfluid transition that occurs in the absence of Bose-Einstein condensation. I will also discuss out-of-equilibrium properties of these atomic 2D gases, in connection with the so-called Kibble-Zurek mechanism.