  We introduce an event-by-event pQCD + saturation + hydro ("EKRT") framework
for high-energy heavy-ion collisions, where we compute the produced fluctuating
QCD-matter energy densities from next-to-leading order (NLO) perturbative QCD
(pQCD) using saturation to control soft particle production, and describe the
space-time evolution of the QCD matter with viscous hydrodynamics, event by
event (EbyE). We compare the computed centrality dependence of hadronic
multiplicities, p_T spectra and flow coefficients v_n against LHC and RHIC
data. We compare also the computed EbyE probability distributions of relative
fluctuations of v_n, as well as correlations of 2 and 3 event-plane angles,
with LHC data. Our systematic multi-energy and -observable analysis not only
tests the initial state calculation and applicability of hydrodynamics, but
also makes it possible to constrain the temperature dependence of the shear
viscosity-to-entropy ratio, eta/s(T), of QCD matter in its different phases.
Remarkably, we can describe all these different flow observables and
correlations consistently with eta/s(T) that is independent of the collision
energy.
