Probing the nuclear equation-of-state and the symmetry energy with heavy-ion collisions

The present status of studies aimed at constraining the nuclear equation of state with heavy-ion collision dynamics is presented. Multifragmentation phenomena, including their isotopic distributions, charge correlations and emission time-scales, may revel the existence of liquid-gas transitions in the phase diagram. Exploring the isotopic degree of freedom in nuclear dynamics is then required in order to constrain the equation of state of asymmetric nuclear matter which presently represents a major priority due to its relevance to both nuclear physics and astrophysics. Some observables that have successfully constrained the density dependence of the symmetry energy are presented, such as neutron-proton yield ratios and isospin diffusion and drift phenomena. The reported results and status of the art is discussed by also considering some of the present problems and some future perspectives for the heavy-ion collision community.