I have received offers from Yale, Cornell, and Michigan Ann Arbor for PhD programme, and I'm not quite sure where to go. I'm interested in differential geometry and topology, and in those areas, Michigan and Cornell clearly have a larger number of people. On the other hand, the two people at Yale I'm interested in working with are good advisors from what I've heard from their advisees.

My undergraduate advisor mentioned that I'll have a much stronger peer group if I go to Yale, as compared to Cornell or Michigan, though I'm not sure how true that is. On the other hand, I've heard that at Yale, barring a few professors, most professors are reluctant to take students. Again, I'm not sure how true this is, but if so, it's rather worrying.

Anyways, what I would like to know is what place would be a good place for studying differential geometry and topology. And if someone who did their undergraduate (or post graduate) degree at one of these places has any other information that might be useful, please do: I'd be quite grateful. Thanks.