Postby **pyfgcr** » Thu Mar 26, 2015 3:54 pm

I can say a little about these places from the point of view of algebraic geometry, narrowly construed; I don't know anything about nearby areas. As you say, the choice of advisor will be important at any of them. All these places have well-known people, and I think you can't really go wrong.

I would've guessed Brown is the best-rated of these places overall, but maybe NW wins. For algebraic geometry, the obvious people are Abramovich and Braverman (who is more towards representation theory). There is a good-sized number of grad students, and I think they have a graduate algebraic geometry seminar, which is nice. (I don't know how many students Abramovich has; my impression is a lot, but it might just be that I know them. I think he has a good reputation for getting them jobs.) They also just hired a younger TT person in tropical geometry for next year, and there are rumblings that they are going to make a (very) senior hire in algebraic geometry in the next year or two -- maybe worth asking about!

UCSD has three obvious people, I think: Oprea, McKernan, Izadi. They have an active AG seminar, and I think also enough students for a grad student seminar. I don't think any of them has had enough students at UCSD that you can really get a sense of how they do after. Izadi and McKernan both had students other places, which might be comparable (including some at UCSB for the latter). Maybe they are looking for new students since they haven't been there long -- doesn't hurt to ask! Mark Gross recently left, but his students at UCSD are another possible data point.

Northwestern I know less about; I think the group is smaller, or at least somewhat broader, or at least somewhat disjoint from my interests. I'm not sure there's a dedicated algebraic geometry seminar, though there are certainly algebraic geometry speakers pretty regularly. On the other hand, Popa just moved there, which is a big win. He had some students at UIC. Another plus is that UIC and UofC both have active AG seminars too, so you could see a lot of talks if you ever wanted to. (On the other hand, UofC to NW is probably a lot further than Brown to Boston.)