I have been looking into several different PhD programs in mathematics, and I am trying to keep my options open. After finishing a doctorate, I am open to working either in academia or industry, although I would prefer a teaching job or similar at a liberal arts college. Additionally, I am currently in the US on a student visa in an undergraduate program.
I would say I have a pretty strong resume, and my GPA is quite good (at around 3.7 on the 4.0 scale). I have research experience in combinatorics and data science, as well as independent reading courses, workshop participation and experience at a summer program for prospective PhD students. I have also given several presentations at student conferences.
I have looked at plenty of different schools in the United States. I am from a small state school, and I believe that applying to Ivy Leagues etc, I would probably not stand a chance. Even some top 50 programs I am quite sure I won't get into, although no risk no reward, so I will definitely try.
After talking to my student advisor, she told me that I should definitely have a few safety schools on my list, and that I will do. I started looking into it, and I noticed there are a few R2 universities with mathematics PhD programs that seemed to have professors interested in similar research as I am.
There was just one main concern: if I want to get a postdoc or similar after finishing PhD studies, would going to a R2 university completely kill my chances of doing this? I have been heavily advised against it by some of my peers.
If it matters at all, I am currently mainly interested in research in discrete mathematics and algebraic topology.