I have so far been admitted to three graduate programs in pure math. Without being too specific, all three schools are top-40 programs (one of which is also top 20, and another is top 30) - these numbers have been extracted from the NRC and US news rankings for graduate math programs. As I am an international student, I cannot travel to these places, so I really want to act quickly to free up some of the spots for people on the waiting list. All three schools are solid in my fields of interest (Topology and Geometry). I've also been told that faculty members I might be interested in working with are available to advise students. I would appreciate any pointers - how do I choose? Based on location? Or do I just go by the rankings here? Please feel free to PM me if you are interested in discussing this at length. Thank you.