  Fast cosmological transients such as fast radio bursts (FRBs) and gamma-ray
bursts (GRBs) represent a class of sources more compact than any other
cosmological object. As such they are sensitive to significant magnification
via gravitational lensing from a class of lenses which are not well-constrained
by observations today. Low-mass primordial black holes are one such candidate
which may constitute a significant fraction of the Universe's dark matter.
Current observations only constrain their density in the nearby Universe,
giving fast transients from cosmological distances the potential to form
complementary constraints. Motivated by this, we calculate the effect that
gravitational lensing from a cosmological distribution of compact objects would
have on the observed rates of FRBs and GRBs. For static lensing geometries, we
rule out the prospect that all FRBs are gravitationally lensed for a range of
lens masses and show that lens masses greater than $10^{-5}M_\odot$ can be
constrained with 8000 un-localised high fluence FRBs at 1.4GHz, as might be
detected by the next generation of FRB-finding telescopes.
