Primordial black holes can form in the early Universe from
the collapse of cosmological perturbations after the cosmological
horizon crossing. They are possible candidates for the dark matter as
well as for the seeds of supermassive black holes observed today in
the centre of galaxies. Non linear relativistic hydrodynamical
simulations shows that, If the perturbation amplitude is larger than a
threshold, depending on the equation of state and on the specific
shape of the perturbation, a black hole is formed. In this talk I will
discuss the dependence of the threshold of primordial black holes from
the initial shape of the curvature profile, showing the relation
between the threshold and the inflationary power spectrum. This allows
to compute consistently the abundance of PBHs formed at a given epoch.
Ongoing work shows that the formation of such objects is strongly
enhanced during the QCD phase transition, with a peak in the mass
between 1 and 3 solar masses, which could explain the source of
gravitational waves emitted by light black hole mergers, as observed
in the Ligo/Virgo collaboration.