What would happen to the "ordered" objects of our physical world - crystals, magnets, superfluids - if we lived in a reduced-dimensional space, on a plane for example? The analysis initiated by Peierls in the 1930s showed that thermal and quantum fluctuations would then be of greater importance, preventing the emergence of an order similar to that observed in three dimensions.
But while a conventional "order-disorder" transition cannot occur in reduced dimensions, this does not mean that all phase transitions disappear. The work of Kosterlitz and Thouless, awarded the 2016 Nobel Prize in Physics, has shown that a new mechanism can emerge. The corresponding transition is termed "topological", as it occurs between states that cannot be connected by continuous deformation.
The lecture was devoted to characterizing this Kosterlitz-Thouless transition in physical systems such as cold atomic gases or resonant cavities for light. We demonstrated the essential role of particle interactions in the formation of topological defects such as vortices. We also described a series of recent experiments that have characterized the emergence of superfluid order in these low-dimensional fluids.