Re-applying to Math PhD programs while in first semester of current program. How viable?

Question

I've looked at many of the answers on this site to questions similar to mine, and I've seen a huge variety of answers. My situation is a bit more specific, so I decided to finally make a post and ask about it.

I applied to Pure Math PhD programs this year (for Fall 2021). I was accepted into two, neither of which were my top choices (they were on the safer side). My partner applied to PhD programs in a different field (not math) but we were not accepted anywhere together. We want to reapply to eachothers institutions this fall in order to be closer. In particular there is one school (call it Y) who is strong in my research area and is close to my partner.

Furthermore, the university whose offer I accepted (call it X) is not strong in my research area - there is at most 1 person who I could maybe work with, but even they are not really super in line with my research interests.

To summarize, I have accepted an offer at University X, and am entering the Phd program there this fall. I really want to reapply to school Y both in order to be close to my partner and because the research there is more in line with what I want to study. I also want to apply to some other top programs in my field, since, if I don't get accepted to Y, I would want to at least be somewhere with strong research in my field. My application for this fall will be notably stronger than my application last cycle due to more research and graduate coursework at my undergrad institution. Is re-applying this fall acceptable, or will it be viewed poorly (although I believe I have solid reasons)?

I am seeking advice on how viable this is since there are mixed responses for other questions. Any input is appreciated, but especially if you've experience this yourself or are perhaps a professor somewhere. Thank you!

EDIT: It's worth also nothing that X is "strong enough" in my area and I love the location, so I could be happy there. Just not ideal, really. In particular I came more into my professional interests a bit later in my undergrad, so at the time of applying I wasn't firmly in one area of research (hence, I'm realizing a bit late that it's a little bit of an awkward fit at X).

Answer 1

There is really no answer to the "viability" question. The only thing to do is to apply and make your best effort to be accepted.

But, as you probably already know, getting accepted to a single institution, considering no others, has a pretty low probability of success generally, due to the competition.

But there is really no reason that you should't apply. If you are turned down you are no worse off than now. Most people will, I hope, understand your reasons.

But there may be another path open, if your partner is in a place with several universities in reasonable distance. You might apply to several universities within, say a 50 mile radius. In some places that is a pretty large set of universities. Not everywhere, obviously.

Your partner can take similar action. Maybe you'll get lucky.

Answer 2

Buffy's answer probably covers most of it, but what you are coming across is also known as the two body problem of academia. And I know there are some places that are starting to try to accommodate for this problem (though probably more at the post-doc/professor levels rather than the PhD level).

An alternative that you and your partner could look into is doing a PhD at both the universities (known as a dual PhD). This would make sense for you to also look since there are other universities that are better suited to your field (plus the two body problem). Though keep in mind that you'll probably have to jump through a lot of hoops (though you might be able to motivate your university since having these programs can look good, especially if someone else happens to sort it out for you). This may also be harder during the coursework component of your work but since COVID probably means your courses are already online so ironically you might have had perfect timing.

Answer 3

If you (and your partner, for that matter) want to have options available, apply and shoot your shots at multiple institutions that you are both interested in as far as research goes. If University X is the best fit of the ones where you accepted, no harm in starting there and exploring the field that that advisor researches in. Maybe a few months in you'll have a better idea of whether that field is really a fit for you (and you may want to even stay there), or not. This, ultimately, however, will boil down to whether you and your partner find it worth the time to try transferring to another PhD program (i.e., you NEED to know that where you are now is not a good fit both in the short-term and the long-term)

Another point worth mentioning, is even if you don't feel this field is the perfect fit for your PhD thesis, if it is still in line enough, is maybe master out of this program (if it is an option at institution X, of course) after exploring the field a little bit. This way you don't burn so many bridges abruptly, and you get to explore multiple different fields right before committing to one. (A good amount of people do this, after a year or two in a PhD program they realize that devoting 5+ years into academia isn't the right fit for them)