<p>Like I know a few professors who I have worked with at a certain Ivy who would absolutely KILL to have me at the school and continue to work with them (I have published research, internships, etc etc), but how exactly would I convey this on an app?</p>
<p>If the school you are applying to accepts supplemental recommendations (check; some schools explicitly state they do not accept, or “strongly discourage” the submission of extra material) ask your prof to write you a letter of recommendation. To make sure it makes it into your file, I would make sure the letter includes your full name, date of birth, and maybe the application ID you used?</p>