NYU likes applicants from S's high school. So each year, there are quite a few students from his HS scattered throughout the various schools of NYU. S has not met up with anyone from his school on a day to day basis. But, of course, that depends on the classes you and the other student sign up for, as well as your dorm assignment and places both of you frequent.
I think some of the posters are right in saying that you just meet it head on if your paths cross. You can just move on; you do not have to mingle with this person. Even if you find yourself in the same class, you can just seat away from the person or make sure not to be in the same work group, if the person is so detestable to you.