Prof. J. Dalibard heads an experimental research group at CNRS-ENS and Collège de France, Paris. Pioneering recent achievements include the first observation of a Kosterlitz-Thouless transition in 2D Bose gases and studies of vortex dynamics in rotating condensates. Early in his career, J. Dalibard was responsible for key theoretical ideas in laser cooling and trapping, including polarization gradient cooling and the Magneto-optical Trap (MOT), and thus provides in his present work the link between theoretical and experimental quantum optics. He has also pioneered theoretical methods to solve the dynamics of open quantum systems utilizing quantum trajectories. Among his honors we can find the Pascal Medal of the European Academy of Science (2009), the Max Born Medal of the American Optical Society (2012), the Davisson–Germer Prize of the American Physical Society (2012), the Senior BEC award (2017), and his fellowships in the European Academy of Science, the Optical Society of America and the American Philosophical Society. Abstract: 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 would not occur, because of the increased role of fluctuations. However non-conventional "topological" transitions can still take place, as understood initially by Kosterlitz and Thouless. During the last decade, a novel environment has been developed for the study of low-dimensional physics. It consists of cold atomic gases confined in tailor-made light traps, forming thus a thin layer of material particles. In this talk I will present some key aspects of these quantum 2D gases, such as their transition to a superfluid state and their (approximate) scale invariance. I will also discuss out-of-equilibrium features, like the nucleation of random currents when merging independent samples. The event will be livestreamed from the ICTP website. All are invited to attend.