Equation of state, flow, fluctuations and J/ψ suppression

Radial flow observed at AGS/SPS energies is very strong, with collective velocities of matter reaching about 0.5c for central collisions of the heaviest ions. The lattice-based Equation of State (EOS) is however rather soft, due to the QCD phase transition. We show that both statements are consistent only if proper kinetic-based treatment of the freeze-out is made. In fact chemical and thermal freeze-out happen at quite different conditions, especially at SPS. Event-by-event fluctuations can shed new light on this problem. We also propose new model of "anomalous" J/ψ suppression found for PbPb collisions, related it to prolonged lifetime of dense matter due the "softest point" of the EOS.