I am currently creating a list of graduate schools to apply to this coming winter. Picking reach schools has been easy, but choosing reasonable and safety schools has been a lot harder for me. I was hoping someone would have some suggestions of schools to look into. I am very interested in topology and I see myself ending up in either low dimensional topology or algebraic topology as my area of specialization. Ideally my "reasonable" schools all have a strong topology focus with a good number of topologists in both fields so I would have a chance to feel out both branches. Here is my list so far:

Just for kicks:

MIT, UC Berkely

Reach:

Columbia, UM Ann-Arbor, Brown, UT Austin

Reasonable:

Stony Brook University (SUNY), City University of New York (CUNY), University of Bonn (might actually be reach, I don't know how it stacks up to the American schools)

Safety:

I don't really know, maybe a lower ranking UC like Davis?

If it helps in your suggestions here is my profile:

Undergrad Institution: Non PhD granting state school (CSU, Sacramento).

Major(s): Mathematics

Minor(s): Economics

GPA: 3.94, upper division math 3.98

Type of Student: Domestic Hispanic Male

GRE Revised General Test:

Will take over summer

GRE Subject Test in Mathematics:

Waiting to see results from April test

Program Applying: Pure math with a focus in topology

Research Experience:

1. Statistical REU at my home university in 2011, I originally thought I wanted to do applied math or statistics. No publication and I practically never spoke to the professors again after this was over.

2. REU in groups and geometry this summer at University of Portland, hopefully resulting in a publication and a few talks

Awards/Honors/Recognitions:

Pi Mu Epsilon and Phi Kappa Phi, nothing exciting.

Pertinent Activities or Jobs:

Tutor in my schools Math Lab. Grader for calculus class. I participate in a the weekly topology seminar at my school, I'm literally the only non faculty member who attends.

Any Miscellaneous Points that Might Help:

I will have taken 5 graduate classes before I graduate (2 semesters of algebra, 2 semesters of analysis, 1 semester of topology). I am easily in the top 3 students in my department and should have some very solid letters of recombination, one from a pretty well know topologist. I have conducted two independent studies under my letter writers, one in Galois theory and the other in algebraic topology. I can code in LaTex reasonably well and have some experience in R from the stats REU, but I haven't kept up on that.