Hydrodynamics in heavy ion collisions*

The quark-gluon plasma is a new phase of matter that can be produced by colliding large nuclei at velocities close to the speed of light. When produced in collider experiments, the plasma expands and cools down rapidly, with quarks and gluons recombining into hadrons within $10^{-22}$ seconds. There is evidence that the strength of the interactions within the quark-gluon plasma, as well as its high density, allows it to maintain a fluid-like collective behaviour despite its explosive expansion. Indeed, numerical simulations based on relativistic viscous hydrodynamics have been shown to describe a broad range of measurements from the Relativistic Heavy-Ion Collider and the Large Hadron Collider. Yet this represents an atypical application of hydrodynamics: the quark-gluon plasma is extremely small and short-lived, with considerable spatial gradients and seemingly few constituents. The apparent success of hydrodynamics under these extreme conditions raises questions about our understanding of its domain of applicability, and provides a valuable opportunity to extend our knowledge of the topic. In this talk, I will present an introductory overview of the situation, highlighting recent progress and remaining challenges.