I'm starting to do some research into what grad schools I should apply to this fall for a pure math PhD. I'll be finishing my undergrad in May 2015 with a major in math and minor in physics. I'm not 100% sure what area I want to go in to, but I'm leaning more towards the topology and geometry side of things. I'm currently doing some work in topology (knot theory) and really enjoy it. I am also interested in geometry/topology research that is related to physics. As an example, I think UCSB may be a good fit because they have a research training group in geometry, topology, and physics and they have that connection with Microsoft Research Station Q. Stony Brook is another school I've been looking at.
Here are my stats in case it is relevant:
School: Unknown Midwest state school - doesn't grant math PhDs
Overall GPA: 3.75 Major GPA: 4.0
GRE Verbal: 168, Quant: 162, Writing: 4.0
Research: Currently working on project in knot theory.
Courses: No grad courses since we don't offer PhD. Typical undergrad prep (e.g. blue Rudin, Hoffman & Kunze Linear Algebra, etc).
I'd like to know if any of you have some suggestions of math departments to check out. I'm having a hard time finding places that are a good fit mainly because I don't really know how to tell if a dept's faculty in this area are very strong or not. Thanks.