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There is a faculty member of Princeton's Institute for Advanced Study (a mathematician), whose research is particularly enticing to me. Do faculty members of the IAS take PhD students? If so, should I just contact him directly?

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    Just to clarify: you mean a permanent faculty member, right? The IAS uses the term "member" for postdocs.
    – Matt Reece
    Oct 3, 2016 at 18:36
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    Just as a data point, Phillip Griffiths (former Director of IAS) has been a faculty member of IAS continuously since 1991. During this time he has supervised 7 Princeton theses, as you can see from the Math Genealogy Project. Oct 6, 2016 at 20:33

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Are you a Princeton graduate student already? If yes, ask someone local about both the rules and whether that person takes students regularly.

If you're at another nearby school (Penn, Rutgers, Columbia, etc.), then usually you also need a local official advisor in addition to an outside advisor. Again, seek advice from someone local who works in a similar area.

If you're not already enrolled in grad school then don't worry about this yet. It is very unusual for people to pick an advisor before going to grad school in mathematics. I certainly wouldn't bother someone at IAS if you haven't gotten into Princeton yet since most people don't get in anyway (eg me).

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    Not being at Princeton I don't know the details of the rules, but according to the math genealogy page Witten has served as sole advisor for several Princeton math theses (though not in the last 10 years), so it seems like it's allowed in some fashion under Princeton rules. Oct 3, 2016 at 17:12
  • Don't many undergrad students in mathematics contact potential supervisors even before applying to see at least if they are interested in taking on students? I personally didn't do this, but it seems that the majority did (especially if they had a good idea about what they were doing) and seem to benefit significantly from it. I don't see any reason why you shouldn't email anyone at IAS with a short email stating you are interested in their research, asking if they are taking on students, and asking through what channels you should apply if you are interested in being their student.
    – PVAL
    Oct 3, 2016 at 18:02
  • In physics, it happens regularly that Princeton grad students have advisors at the IAS (with, I think, a nominal official advisor at the university as well). (When I say "regularly," I mean that at any given time there are at least a handful of Princeton physics grad students with IAS advisors, though of course this is a small fraction of all Princeton physics grad students.) I expect, but have no direct knowledge to assure me that, the rules are the same in math.
    – Matt Reece
    Oct 3, 2016 at 18:29
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    @PVAL: It's somewhat unusual for future math graduate students to contact potential advisors before acceptance, especially at a top place like Princeton that doesn't need to put effort into recruitment. What is much more normal is to email or meet with potential future advisors after acceptance but before deciding where to go. Oct 3, 2016 at 18:53
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To be clear, having experienced that environment some years ago, and having observed it relatively recently: yes, math grad students at Princeton are able to have advisors among the permanent members of the IAS math faculty.

... but it is not clear whether grad students at Rutgers or other near-by places could expect IAS permanent math faculty to agree to advising... and I'd wager that those other institutions would want a more "local" co-advisor, for bureaucratic reasons imposed by their universities.

The question of asking whether they're taking students: well, sure, but selectively, and you're not likely to induce a definitive answer about whether they'd take you, especially at such an early stage, unless you are "super-special", which one should not depend on.

You could ask whether, in principle, he'd take students, yes. But the meaning of the answer might be subtler than you anticipate, given peoples' reasonable hesitancy to commit to unknown conditions...

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Appointments and secondary appointments can be tricky, and can differ for different faculty members in the same program. You should ask both the faculty member and the department you'd like to be a student in if the faculty member is entitled to mentor student from that department. Even if not, sometimes comentorships can be arranged to suit an individual case.

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