EQUATION OF STATE, FLOW, FLUCTUATIONS AND J PSI SUPPRESSION/

Radial flow observed at AGS/SPS energies is very strong, with collecti ve velocities of matter leaching about 0.5c for central collisions of the heaviest ions. The lattice-based Equation of State (EOS) is howeve r rather soft, due to the QCD phase transition. We show that both stat ements are consistent only if proper kinetic-based treatment of the fr eeze-out is made. In fact chemical and thermal freeze-out happen at qu ite different conditions, especially at SPS. Event-by-event fluctuatio ns can shed new light on this problem. We also propose new model of '' anomalous'' J/psi suppression found for PbPb collisions, related it to prolonged lifetime of dense matter due the ''softest point'' of the E OS.