The equation of state (EOS) of dense nuclear matter can give insights into fundamental properties of QCD: among others, it can elucidate phases of matter in different regions of the QCD phase diagram, it can help explain the structure of both neutron stars and neutron-rich nuclei, and it can inform us about the nature of the underlying fundamental interactions. In experiments colliding heavy nuclei at relativistic velocities, the EOS is probed through observables describing the collective behavior of the produced matter, such as flow observables, the dependence of which on the EOS can be studied in simulations.
In this talk, I will discuss recent progress on constraining the EOS with hadronic transport simulations, used to model heavy-ion collision experiments at intermediate energies. I will highlight results from a recent Bayesian analysis study using new data from RHIC, and I will discuss the findings in the context of other known constraints from heavy-ion collisions and neutron star studies. I will also outline developments in state-of-the-art hadronic transport codes necessary to fully utilize the potential of the forthcoming wealth of data from the BES-II FXT program at RHIC, from GSI and FAIR, as well as from FRIB and future FRIB400
