Hello, I'm new here, but I've peeked at the admission results posts a few times and figured this would be a good place to get advice. I'm currently finishing up my master's and I'm planning on applying in the next month to PhD programs. I did my bachelor's and master's at the same institution (not a well known one) and my interests are in geometry and/or topology, but I'm not entirely sure of any specific area. I'd like to apply to Stonybrook, so any advice on that would be welcome (since they seem kind of arbitrary based on regular admissions stats).
I got 72nd percentile on the MGRE, I had a 3.9 GPA coming out of undergrad, and I'm at around a 3.8 in my master's. I did an REU in geometry (I guess I might call it differential geometry, but it was really a programming project), I attended a mathematical general relativity workshop at MSRI this last summer, and I'm currently working on my master's thesis in computational geometry. I've taken some basic courses in differential geometry and algebraic topology, but not enough for me to really know what I'd like to do specifically (which makes shopping around for advisers kind of hard).
Right now I'm planning on applying to SUNY Stonybrook, the big state universities in my home state, and the university where my thesis adviser went. Any other suggestions? I'm not really sure what is a reach, what isn't, or what would be a good choice for someone with my general interests.