What are some good universities in the USA for a PhD in topology/analysis?
I have researched for them on the internet and was able to sort some top 11 universities.
1) University of California--Berkeley, Berkeley, CA
2) Harvard University, Cambridge, MA
3) Princeton University, Princeton, NJ
4) Massachusetts Institute of Technology, Cambridge, MA
5) University of Chicago, Chicago, IL
6) Stanford University, Stanford, CA
7) University of California--Los Angeles, Los Angeles, CA
University of Texas--Austin, Austin, TX
9)Columbia University, New York, NY
10) Stony Brook University--SUNY, Stony Brook, NY
11) Cornell University, Ithaca, NY
Can someone suggest me some mathematics department which are ranked higher on research for topology and analysis but do not have so good overall university ranking?
For example, SUNY, Stony Brook has one of the best topology department in the US, but the overall ranking of university is not so good.