advanced studies and chances of admission

what is the best way to reflect the advanced studies someone has done in a particular subject - for example astrophysics covering spectroscopy, steller structures, evolution of starts , h-r diagram , black holes , binary stars , cosmology, hubble constant , relativity, special relativity with reading from various books by the reputed physicists

any insight is greatly appreciated

also will the chances be significantly higher due to the advanced studies of a particular subject

BTW i am referring to chances in Columbia, CMU or UChicago