The Stellar and Sub-Stellar Initial Mass Function
The IMF is not a single power law, but rather, continually changes its slope below masses of a few Msun.
Thus far, no low-mass cutoff has been observed.
Uncertainty about a high-mass cutoff: given all the massive stars we know about, should we have seen a 1000 Msun star by now as predicted by single power law?
Goal is to relate constraints on IMF form, shape, and mass limits to the physics of star formation.