Postby kingcrimson » Tue Feb 14, 2012 1:50 pm
This probably isn't the answer you were hoping for, but Algebra is a rather large area of study. Note, for example, DanielMcLaury's comment on his 2012 application data: his school (Oklahoma) heavily focuses their Algebra research in Representation theory, yet he would rather research Commutative Algebra and Algebraic Geometry. My guess is that the schools on the US News rankings are probably strong in many areas of Algebraic research, and if you are unsure of what area of Algebra interests you, those would be your best bets. Smaller schools tend to focus their research in more specialized areas.
If you do have some idea of which areas interest you, I recommend finding the website of a mathematical journal researching that area and finding out who is on the editorial board. For example, I am interested in Lattice theory and Universal Algebra, so I looked up the editorial boards for "Order" and "Algebra Universalis," respectively. By doing that I came across Colorado and Vanderbilt as potential schools.