Statement of purpose: how to give motivations for applying to a certain graduate school without stating the obvious or gratuitous flattery?
This could be a good opportunity to mention particular faculty there you might want to work with, if there are any such. (But don't go overboard, or say anything that's not true.) In any case, in my experience, these sections generally don't affect decisions -- with the one big exception that if you say you want to come to study geometry, and the committee knows that all 3 geometers in the department are retiring, they might not admit you for your own sake. (Another reason not to say anything that's not true!)