What are the different mathematical cultures out there? That is, what universities focus on what fields and subfields in mathematics? [closed]

Question

I am a soon-to-be undergraduate: a double-major in mathematics and computer science (but I have plenty of graduate-level mathematics courses I was advised to take by several professors).

However, since I do plan to pursue a career in research (i.e. I will apply to PhD programs), I can't help but wonder what cultures or what concentrations do major universities have? That is, what universities focus on what fields and subfields. While it is true that I can research this information on my own, which I definitely will, I was wondering if I could get some perspective on this from people that are frankly more qualified than me (and have more experience dealing with different universities).

This could potentially help me with applying to different REUs, as well as applying to graduate school in the future. I would appreciate any information, as I think you could help me gather more information (anecdotes are also welcome!).

For reference, while I do not know what I want to pursue later on, I do prefer more pure-mathematical topics when compared to applied mathematics (not to say I can't enjoy the latter), especially more group-theoretic and topological things.

Thank you! I would appreciate any kind of information.

Answer 1

In the US, at any large R1 university, especially State universities, perhaps, you will find very wide coverage of mathematics. At a minimum, there will be lots of choices for students to choose a subfield. Many faculty will have more than one interest as well. But, if there are fifty or so faculty members then you have a lot of choice.

An exception might be if a field or subfield is less than ten years old. It takes a while to build a faculty and it takes a while to change focus. Otherwise, I'd focus on other things in looking for a graduate school in math.

All of the fields you mention in your profile are certain to be covered.

Answer 2

Your question is of such a general kind that it is hard to offer a reasonably concise answer to it.

On the other hand, I see that you are trying to glean information, which may be of use to you when you have to choose a grad school, a scientific advisor, etc.

So here is a word of advice. While it is highly advantageous for a graduate student to work under the guidance of a highly acknowledged and prominent academic, it is important to keep in mind that great scholar and great adviser are not synonyms. I unfortunately know some great scientists who will offer to their disciple a problem to solve, and will prefer not to be bothered except when the problem is solved. Stay away from such folks, no matter how celebrated they are. It is a safer bet to work under a professor (even a less known one) who is regularly spending hours with his or her students and postdocs, actively helping them in their research.

Last, and by no means least, when choosing an adviser, make sure to explore the careers of his or her former graduate students. If you find that after graduation all or almost all of them received postdoctoral positions (ideally, postdoctoral fellowships) at decent places -- this will be a clear sign of a wonderful adviser, even if (s)he is not a member of the National Academy.