I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, elliptic curves); but I still don't know enough to make any definite statements.
I have done a good amount of research on the different graduate schools, but I am hoping for some advice from people more involved in the field. What are some universities with good graduate programs in mathematics, and in particular algebra and algebraic number theory? Where is the interesting research going on in those fields?
I have seen the US News list on best algebra/number theory/algebraic geometry grad schools. And have looked into the research in Princeton, MIT, UC San Diego, Stanford, Berkeley, Brown, University of Chicago. So I was hopping for answers of less known universities, or more information about the known ones which is not easily available.