  Spatial structuring of an optical pulse can lead in some cases upon free
propagation to changes in its temporal profile. For example, introducing
conventional angular dispersion into the field results in the pulse
encountering group-velocity dispersion in free space. However, only limited
control is accessible via this strategy. Here we show that precise and
versatile control can be exercised in free space over the dispersion profile of
so-called `space-time' wave packets: a class of pulsed beams undergirded by
non-differentiable angular dispersion. This abstract mathematical feature
allows us to tune the magnitude and sign of the different dispersion orders
without introducing losses, thereby realizing arbitrary dispersion profiles,
and achieving dispersion values unattainable in optical materials away from
resonance. Unlike optical materials and photonic structures in which the values
of the different dispersion orders are not independent of each other, these
orders are addressable separately using our strategy. These results demonstrate
the versatility of space-time wave packets as a platform for structured light
and point towards their utility in nonlinear and quantum optics.
