Hosted by: Heikki Mantysaari

The past years have seen tremendous progress in the description of Quantum Chromodynamics at vanishing and finite temperature and density with functional approaches, such as the functional renormalisation group or Dyson-Schwinger equations. Within these approaches QCD correlation functions of quarks, gluon and hadrons are computed non-perturbatively from first principles. In the talk I will discuss results for the phase structure of QCD at finite temperature and density, as well as for thermodynamical obserables such as the pressure and the trace anomaly. The approach is also applied to baryon number fluctuations. By now functional approaches also allow for a direct computation of transport coefficients in QCD. First results concern the temperature dependence of the shear viscosity over entropy ratio in Yang-Mills theory and QCD. The talk concludes with a discussion of the further prospects for our understanding of the phase structure and dynamics of QCD.