After just completing my PGRE and seemingly not getting the definitive victory I had hoped, I seem to be at a loss to where I should bother applying for grad school.
My primary disadvantage is that I went to a very mediocre school and underachieved first 3 semesters (for reasons that are personal but somewhat excusable). Since then I have had only one B in any class (a 4.0 in physics). By the end of this semester I will have taken 2 grad courses for a grade and audited a general relativity class. Also I will take a grad QFT class and differential geometry course in my last semester. I will graduate with two degrees a BS in Physics and a BS in Mathematics. I have only one year of research, but with that research I am currently the sole author on a paper currently in review at Journal of Mathematical Physics. Like many people I am interested in QFT and gravity, but I would prefer to approach them from a more formal standpoint. I would love to get into the most rigorous programs but I feel my undergraduate education is slightly lacking in some areas (I have not taken a topology or a functional analysis course; my math credits basically cover a year of real analysis and algebra, PDE, basic complex, and a bunch of peripheral courses).
Let's suppose the paper goes through and I get very good recommendations from some respectable physicists
my general GRE scores are: quant-800, verbal-680
my overall GPA is 3.7+ and Physics is 4.0
Also I am a Sigma Pi Sigma inductee
Lets suppose my PGRE percentiles are anywhere from 70-95 (don't feel too confident about my PGRE)
What is the best Mathematical or high energy theory program I stand a fair chance at getting into?