Finding Math Graduate School by Interest

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SpaceWalrus
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Graduate school applications are steadily approaching, and I am begging to investigate different institutions to apply to for math. Right now, I am performing a coarse inspection of schools, based on a few criterion. One of the more important of which is how strong they are in different fields. I would like to know the top schools in my areas of interest (namely analysis, algebra, differential equations). My hope is to find some interesting research at these schools.

I have looked at a few different rankings, such as the one provided by U.S. News. However, I have a feeling that many of these lists value prestige over strength. I understand the list I seek isn't exactly a quantifiable one, and will have biased elements. Regardless, I was curious if anyone had any advice on how to search for schools by category. Thanks.
 
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You should talk to the experts in the fields you're interested in at your school. They will have much better knowledge of what schools are strong in what areas than any rankings you'll find online.