The Astrophysics of Star Formation Across Cosmic Time at $\gtrsim$10 GHz
  with the Square Kilometre Array
  In this chapter, we highlight a number of science investigations that are
enabled by the inclusion of Band~5 ($4.6-13.8$ GHz) for SKA1-MID science
operations, while focusing on the astrophysics of star formation over cosmic
time. For studying the detailed astrophysics of star formation at
high-redshift, surveys at frequencies $\gtrsim$10 GHz have the distinct
advantage over traditional $\sim$1.4 GHz surveys as they are able to yield
higher angular resolution imaging while probing higher rest frame frequencies
of galaxies with increasing redshift, where emission of star-forming galaxies
becomes dominated by thermal (free-free) radiation. In doing so, surveys
carried out at $\gtrsim$10 GHz provide a robust, dust-unbiased measurement of
the massive star formation rate by being highly sensitive to the number of
ionizing photons that are produced. To access this powerful star formation rate
diagnostic requires that Band~5 be available for SKA1-MID. We additionally
present a detailed science case for frequency coverage extending up to 30 GHz
during full SKA2 operations, as this allows for highly diverse science while
additionally providing contiguous frequency coverage between the SKA and ALMA,
which will likely be the two most powerful interferometers for the coming
decades. To enable this synergy, it is crucial that the dish design of the SKA
be flexible enough to include the possibility of being fit with receivers
operating up to 30 GHz.
