Graduate programs for algebraic geometry and algebraic topology

Forum for the GRE subject test in mathematics.
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Graduate programs for algebraic geometry and algebraic topology

Postby grassman1 » Wed Mar 16, 2016 3:46 pm

What are the top graduate programs to apply to for algebraic geometry and algebraic topology? Preferably, I would like to work at the intersection of the two areas, and there seem to be much activity in fields such as derived algebraic geometry, motivic homotopy theory, etc. What other areas are active at the intersection, involving applications from one field to the other, or combining the two, and what are the best graduate programs to look at for them? In particular, it would be ideal if the program also had people working on applications of these two fields to mathematical physics/quantum fields and strings, but not necessary.

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Re: Graduate programs for algebraic geometry and algebraic topology

Postby joga » Fri Mar 25, 2016 10:28 pm

If you know that you want to work on areas like Motivic Homotopy Theory, K-Theory, Derived Algebraic Geometry etc I would want to believe that you have spent some time with these subjects, and would automatically know the names of people who work on these problems. If these niche subjects catch you fascination but you do not have experience then the best thing would be to apply to programs with strong generic math backgrounds and learn the mathematics and see where you go from there. For that your teachers would be best judge. You do seem very inexperienced with background material requesting for groups applying these techniques to physics etc, which though they exist but are very niche and very intertwined.

An experienced person would know that for these niche areas especially in the US, you would rather want to apply to people to work with rather than top places. Eg. Princeton or Columbia or MIT for that matter does not have anyone really doing K-theory, or Motivic Homotopy theory. But they are all TOP schools. Likewise Chicago or UCLA i think do not have any Kollar type birational algebraic geometer or Gromov Witten theory - correct me if i am wrong (I am pretty sure about UCLA) . But these are among the top 10 places i can think of, for doing algebraic geometry in america, I would throw in Harvard, Michigan and Berkley.
Because if you know that you want to do there are people at many places which are fantastic per say but there are hardly any groups unlike some places in Germany and France.
So the best way is to learn these subjects if you can before you apply (by learn i mean atleast get a feel).

I hope i did not come across as rude.

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Re: Graduate programs for algebraic geometry and algebraic topology

Postby TheGreenBook » Sat Mar 26, 2016 11:30 am

I agree with joga that if you actually know the area you want to go in, you should probably have an idea of who works on it and where to apply. However, there is also the chance that you do know some people and places, but you just want some more options. In this case, I think it is acceptable to email the people you do know of and ask for recommendations. I had a graduate student advisor for an REU who did this. He wanted to work in computational algebraic geometry, but knew he wasn't going to be able to get in to top places like Berkeley, so he emailed a faculty member at Berkeley, explained his grades and research experience, and asked the faculty member for ideas of where would be a good idea to apply. He got good recommendations, and ended up at the place where he acted as my advisor.

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