The QCD phase diagram and heavy ion collisions from lattice QCD

The QCD phase diagram is an important ingrediant to understand both the develpment of the early universe and the results of recent heavy ion collison experiments. At zero baryon density lattice QCD is an established tool, that provides precise theoretical results. Calculations at non zero densities however require new techniques to deal with the sign problem. In this talk I will review our recent effort to investigate QCD at non-vanishing baryon chemical potential.