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So I'm interested in a PhD in math, and my research area is in set theory. Kind of a niche place to be. Forcing, large cardinals, determinacy, etc. I know that the biggest schools (Carnegie Mellon, Ivies, MIT, etc.) have these researchers, but I'm not sure where to start searching for these programs? Is there any place to search for PhD programs by the fields of mathematics they sponsor? If you know anything about contemporary set theory, you could chime in, but even if not, let me know what the best ways to search for faculty are.

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    Apart from other things, UC Berkeley has a great tradition in set theory, if by some chance you didn't know. And/but not really all the Ivies. Styles change... Sep 13 at 1:04
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    That list wasn't supposed to be all-inclusive, and also was just a general "I'm looking for not-top-25 schools" sort-of thing. But yes, there's some excellent faculty at Berkeley. I'm looking for places that are safer "in"s for me, if that makes sense. And a systematic way to check this, if possible.
    – Luna145
    Sep 13 at 1:09
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    A good idea is to email one of those researchers and just ask them.
    – k99731
    Sep 13 at 1:21
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    Assuming this is for U.S. schools (based on your examples), can't you just visit the web pages of the "not-top-25 schools" and look at their research areas and faculty interests? I can't imagine this would take more than a few hours at most. I did this in Fall 1985 and Winter 1985-86 (well before the internet; same field, also non-top schools), and I think I just flipped through journals and books like this, looking at author affiliations. Of course, I was already familiar with where many such people were from (continued) Sep 13 at 4:16
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    Look at the authors of set theory papers in mathsci.net and arXiv.
    – markvs
    Sep 13 at 5:59
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The American Math Society does publish something about recent PhD's, but I'd be mildly surprised if it were searchable.

The math genealogy project has an "advanced search" that can indeed search with many different filters. I'd look for "set theory" PhD's in the last 5 years (or so), and see where they were granted. Then filter those places on "exclusiveness" if that is a concern... which is entirely reasonable, after all.

Faculty at your current place should have some idea about that exclusivity, even if they don't know current events in set theory.

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There are two basic approaches that I think might yield good results for you.

My first suggestion would be to try and find some relatively recent publications in the field of study you are interested in pursuing. This would give you some specific faculty to consider/contact. Even more importantly, these faculty are active researchers in the field and if they have grad student co-authors, that bodes well for the students who study under them.

The second is that research areas tend to be small communities. If you happen to have a contact in that field, perhaps one of your professors at your current institution or one identified from publications as described above, they likely can give you names of others to contact. Most educators are interested in helping out students and would be willing to share their expertise, but do spend some time doing research on your own beforehand that you could share. E.g., "I saw publications by Dr. X at School A and Dr. Y at School B, but do you know of anyone else I should be considering?"

Keep in mind that not all professors are taking on new graduate students and not all "big names" in the field are active researchers. I'm sure there are a number of other questions on here that talk about how to pick an advisor. But that's a problem to tackle once you know what your options might be.

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  1. If you want to find top schools, US News and World report ranks graduate programs in math, and it lists top schools by discipline. In particular, one of the disciplines it has is Logic:

https://www.usnews.com/best-graduate-schools/top-science-schools/logic-rankings

These rankings don't necessarily match too closely with expert opinions, but it gives you one place to start looking.

  1. For finding more schools, Math Departments often have Faculty Research Interests pages, so can just do a web search for something like

mathematics departments faculty research interests "set theory"

My search engine of choice results in a lot of different schools/faculty.

  1. If you know active faculty in the area, ask them for suggestions. Or if you don't, you can look websites of recent conferences in Set Theory and see where people are from.
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The AMS has a "Find a Graduate Program" website that lets you search by very broad categories. See

https://www.ams.org/find-graduate-programs?prog_type=PHD

Unfortunately, the categories are relatively broad and none of them mention Set Theory. This says something about the current level of interest in Set Theory.

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  • Well, it looks like Set Theory would be looped into the Discrete Math/Logic/CS category. But do you know how the AMS determines these categories?
    – Kimball
    Oct 14 at 15:54
  • Departments self enroll themselves on this web site based on their own ideas about what areas they support. The AMS isn't saying anything about the strength of the programs in different areas. Oct 14 at 16:26

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