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.
Yale, Cornell or Michigan for geometry PhD?

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 Joined: Wed Mar 14, 2018 12:41 am
Re: Yale, Cornell or Michigan for geometry PhD?
Michigan is not an ideal place for differential geometry and topology. I do not think there is any person who is still active in differential topology. There are indeed several people relevant to differential geometry who are still active: Prof. Sarah Koch, Prof. Lydia Bieri, and Prof. Ralf Spatzier for example. But they do not really focus on what a typical differential geometer does. I would advise you against Michigan if you really want to do differential geometry/geometric analysis also because students here mostly do stuff related to algebra/algebraic geometry, and you will have few fellow students to talk to if you are interested in differential geometry.
Also, in terms of overall strength, Michigan and Yale, are certainly stronger than Cornell. But unfortunately, I do not think Yale is strong in differential geometry either. But those are of course all good schools. It is my impression that Yale is traditionally strong in representation theory.
Also, in terms of overall strength, Michigan and Yale, are certainly stronger than Cornell. But unfortunately, I do not think Yale is strong in differential geometry either. But those are of course all good schools. It is my impression that Yale is traditionally strong in representation theory.

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 Joined: Wed Mar 14, 2018 12:41 am
Re: Yale, Cornell or Michigan for geometry PhD?
@Taylor. What do you mean by "what a typical differential geometer does"? As far as I've seen of their current work, it seems to me the kind of stuff differential geometers would do (as far as I can tell given the little amount I know). I talked to Ralf Spatzier, and he said there are a fair number of people doing geometric analysis, and other aspects of differential geometry.
Re: Yale, Cornell or Michigan for geometry PhD?
I am sorry. That might be the wrong term to use. Differential geometry is a vast area and it is really hard to say what a typical differential geometer does. However, I am personally inclined towards the flavor of works of people such as Donaldson, Valentino Tosatti, and Song Sun etc. If you look at Prof. Ralf Spatzier, I think most of his works focus on questions arising from dynamics, which are different from the works of persons that I mention.
Michigan has a strong math department overall, and Prof. Ralf Spatzier is very good. The grad courses here are very complete as well. However, they offer relatively fewer choices for geometry compared with other disciplines. But that can always be compensated by doing a reading course with a professor you like.
Michigan has a strong math department overall, and Prof. Ralf Spatzier is very good. The grad courses here are very complete as well. However, they offer relatively fewer choices for geometry compared with other disciplines. But that can always be compensated by doing a reading course with a professor you like.
Re: Yale, Cornell or Michigan for geometry PhD?
Did you apply to UPenn? Since based on your interest, UPenn would be a perfect fit for you.

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 Joined: Wed Mar 14, 2018 12:41 am
Re: Yale, Cornell or Michigan for geometry PhD?
@gragragra. Unfortunately no. I only applied to places I knew at least one of my recommenders had colloborators; I thought I didn't stand a change of getting in otherwise. In retrospect, I should have had been a little more ambitious.
Re: Yale, Cornell or Michigan for geometry PhD?
Kk, I see. All of them are great programs. It really depends on who you want to work with though. (I might choose Michigan)