Emergence near the temperature zero point: Topological quantum liquids

Quantum mechanics holds many surprises in store - a recurring experience not only for physics students in their first semesters, but also one that constantly gives new impetus to current research. For example, when the interaction of a large number of quantum mechanical degrees of freedom conspires in a subtle way and leads to qualitatively completely new effects and material properties. A particularly fascinating emergent phenomenon of this kind is the emergence of topological order. In this colloquium, I will report on the current search for topological order in a variety of physical systems, the hopes for the use of topological matter in quantum computers, and all the small and large hurdles on the way there - for example, in the form of all those instabilities of topological order caused by disorder, which are a new source of precisely that fascination of quantum mechanics.