Rankings as a metric for the competitiveness of admissions

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eok20
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Hi, I was wondering how strong the correlation is (adjusting for size of program) between a mathematics departments ranking (e.g. from US News) and how hard it is to get admitted to the PhD program. I am asking because as of now my safety school is ranked in the high 40s and is fairly big (around 60 graduate students). Besides this one, I am applying to one top 10 and three top 25. It has been hard for me to find additional schools that I have a chance of getting into that are active in the area I'm interested in (mathematical physics/differential geometry). I have a 4.0 from a decent state university, a fair amount of research experience, and I'm guessing my subject GRE will be between 70-90 percentile. Can I bank on at least getting into my safety school? Would it be appropriate to e-mail the graduate director asking what the stats of a typical admitted student looks like?

Thanks so much!
 
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You have a 4.0, some decent research experience and a pretty good GRE. Of course you have some pretty good chances of getting in. You'll probably get in at least some of your top 4 picks as well, depending on how many students they're taking this year and the likes.
 
Yeah, your record sounds spotless. It looks like the only thing that could weigh you down is the subject GRE, but even 80-90th percentile is very good. I think you should apply to as many top programs as you can afford.