Transport and thermalisation at NLO from kinetic theory

In this talk I will review the effective kinetic description of QCD and show how it can be used to determine the transport coefficients of the QCD medium, such as the shear viscosity, and to study how thermalisation, i.e. the transition from the initial nuclear state to a near-thermal medium, takes place in a weak-coupling scenario. I will then show how this kinetic description can be extended beyond leading order in the QCD coupling, owing to recent theoretical developments in the understanding of light-like separated thermal amplitudes. I will then show the results from the numerical implementation of this NLO collision operator, both for transport coefficients and for thermalisation in an idealised setup, and I will discuss the impact NLO corrections have on the stability of these observables.