The QCD phase diagram, universal scaling, and Lee-Yang zeros

We will report on current progress in the understanding of the QCD phase diagram, including universal scaling in the chiral limit and the vicinity of the QCD critical point. In the latter case we will discuss the universal scaling of Lee-Yang zeros and their determination from multi-point Padé approximations to the baryon number density at imaginary chemical potentials. In particular, reported results include the critical phase transition temperature, the curvature of the critical and pseudo-critical transition temperature with respect to the chemical potential and the location of the QCD critical point.