Contacting potential advisors before applying to graduate program - PURE MATH
The expected behavior here is that you talk to faculty after you’ve been accepted to the program, not before.  That way you have more information to make your decision about where to go, but faculty aren’t spending a lot of time with students who aren’t going to be accepted.
Contacting a faculty member is unlikely to give you an advantage in admissions if you don’t already know them, what can give an advantage is if you have a mentor who knows faculty at the school you’re applying to and puts in a good word.  It’s not likely to hurt you either, as long as you’re polite about it, but you’re likely to get no reply or a short reply saying that they’re not on the admissions committee.  They’re more likely to be annoyed than to help, but in 9 cases out of 10 it just won’t amount to anything.