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.