  We consider the coherent control of ultracold molecule-molecule scattering,
impacted by a dense set of rovibrational resonances. To characterize the
resonance spectrum, a rudimentary model based on multichannel quantum defect
theory has been used to study the control of the scattering cross section and
the reaction rate. Complete control around resonance energies is shown to be
possible, but thermal averaging over a large number of resonances significantly
reduces the extent of control of reaction rates due to the random distribution
of optimal control parameters between resonances. We show that measuring the
extent of coherent control could be used to extract meaningful information
about the relative contribution of direct scattering versus collision complex
formation, as well as about the statistical regime.
