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Lately I have been developing a good relationship with Prof. Wright.

She has clearly* gone out of her way a few times to help me, having a very pleasant, generous, and kind personality. Prof. Wright is searching for students (in her university of course, undergraduate, Master, or PhD). I really like her research and would love to work in her area. However, there's no researcher working in the field anywhere near** the university I study at.

This brings the reason for this question: I have been thinking about
asking her if she could advise me.

1. Is this unreasonable?


2. If not, how unlikely is it for her to accept? (To make this practical: what would you do if you were in her shoes?)


3. Is there a chance of this ruining our relationship? If yes, what can I do to make sure it won't ruin it?


4. Finally, if I'm going to ask her to be my advisor, it won't (of course and unfortunately) be in person, which means email. What can I do to enhance my chances here?

A few remarks which are (probably) important:

1. Of course such a setting should benefit both people! I would like to contribute to her research, in a way that is useful to her too;


2. My field is in Mathematics, being purely theoretical and not requiring lab/field work;


3. 
   

   I am moderately independent when it comes to research. More details (in view of comments/answers on this point):

   
   
   

   3a. In terms of learning: I've been learning graduate topics by myself for the past two years (I also learned the prerequisites for them in the same way). In particular, I'm used to approaching new topics and learning them by myself.

   
   
   

   3b. In terms of producing: I believe*** I would be capable of producing a review article on recent (<10 years) research on certain topics in my field by myself. On the other hand, I can't produce original research. This means I'm used to academic writing, somewhat used to reading original research papers and slightly used to asking original research questions (i.e. can this work be extended for such and such case, what are the main problems this would entail, etc.), but have zero experience with actually producing new research.

   
   



4. I can't move to (anywhere near) her university for now.




5. (In view of anon's answer) I really don't mind if this won't count for my degree, or that I will be working unpaid.




6. On the other hand, I will have to do coursework next year, and
   would like to know if (assuming Prof. Wright accepts me as her student) carrying another project while working with her would be a problem either to her, or to my local, next year, advisor, provided that I can handle these two projects concurrently. (In this case, I would choose a not project with my local advisor sufficiently undemanding (yet not "pointless") for this to work.)

This question is heavily lacking some specific details. I can't provide those, for Prof. Wright is in the SE network too (and these might identify myself).

*To prevent against any kind of bias I may have in making this judgment, I have explained my situation to a few people, who agreed this is indeed a(n unusually) good relationship.

**Near here means less than 2000 km (probably even more).

***I have been doing something similar recently.

It's probably not impossible, but distance isn't the only impediment. If you want her to be your formal advisor then you may need permission from both universities and they may need to work out some compensation, depending on the rules. This will be especially the case if she needs to formally approve (perhaps sign) your dissertation.

Distance is a problem of course, but with today's communication options it can be overcome in such a case. But you should also consider the possibility, even the necessity, of working face to face on occasion. One way to do this is through attendance at a conference with an extra day or so to work after or before the conference itself. There are other options, of course, including trying to get a small grant from somewhere to cover travel - either yours or hers.

But asking is certainly appropriate if you are willing to also work to obtain the necessary permissions and deal with the distance issue.

If she is to be only a secondary advisor it is a bit simpler, but needs the buy-in from your main advisor at your current place. This is easiest if the two know one another and are comfortable working together. But there may still be permission and compensation issues to deal with.

Make sure you know at the start everyone's expectations about joint authorship of anything you produce, of course.

Since you have now added that you're an undergraduate, I think it's actually pretty unlikely she will agree.

A few issues:

1. Advising people is hard; advising undergraduates is even harder; and doing that long-distance is basically impossible. Although, you haven't stated your field. Maybe it's easier in your field than mine, or in theory. Still, personally, I would never accept to tele-mentor someone, especially someone I hadn't met in person.




2. In principle, she has a commitment to undergraduates at her university first, before those a continent away. If her department requires research credit (called "499" or "independent study" at my university), that's taking a slot away from one of their majors.




3. If you are required to have a mentor in your department, they most likely won't accept an off-campus one.

Asking won't ruin your relationship, although it might make you seem a little out of touch with what's required from such a relationship.

I think your best bet is to find faculty at your current university who can be your mentor on paper (and can actually contribute!) but is open to working with the distant professor. Maybe you can ask her if she knows anyone in your department.

Collaborating with her now will certainly help you get into her group in graduate school! I'm sure she's happy to have someone excited about her work and wanting to work with her, but I think it's pretty unlikely she can/will do anything official for you.

(Like I said, I don't know your field, but I'm not sure if "but can write an introduction to this area" is "moderately independent.")

I have done my Master's thesis project with a supervisor who was ~700km away, so I can kind of relate to your situation. I will address your questions one after the other:

1. I think it is absolutely reasonable to ask her. Nobody's getting hurt by a kind and polite request for a collaboration / advisory project.



2. Most researchers love to work with motivated students and sometimes it is really hard to find them (especially in niche research areas). Thus, if she is not drowning in other projects or has any formal obligations at her institute that could prevent her from advising external students, your chances should be rather high.




3. yes, there is chance that asking her can ruin your relationship. This could happen, if you ask in a way that seems rather demanding. You have to see it as really asking for a favour and that she has every right to decline even without any reasoning. However, if she is a kind and intelligent person, she probably won't simply decline without any additional information.




4. Your last question is, I think, the most important one. From my experience, the most challenging thing with long distance advisory relationships is to set a clear structure. Things can go in the wrong direction much faster, and it is much more difficult to realize that one has gone astray. Especially if you are an undergraduate student, this is a big issue. Probably, if she declines your request, this will be the most relevant reason.

You can a priori address these problems when making your request by:

• proposing a thoroughly planned proposal structure for your research project. This does not need to be perfect, but should show that you are able to work independently and in a structured manner.


• offering that you will be available for video chat meetings (Skype calls, Google Hangout or whatever) e.g. once a week.


• offering that you will try to meet in person something like once a month. If you cannot offer to come to her in person at all, my guess is that this collaboration won't happen.


• suggesting someone from your university who will be a co-advisor, so that she does not have to work into any of the special formal requirements that your university is demanding (most likely, your university will require you to have one "local" advisor, anyway)

Further, be prepared, that if she agrees to advise you, you will have to work harder and much more independently than if you had a supervisor next door. You should be 100% motivated and absolutely keen to working on this project.

As a last comment, even if it may be true that there is no one in your area who is doing research in this very particular niche, most likely there are other, closely related fields where people nearby are doing great research. As an undergraduate it is somtimes hard to get an overview which topics are closely related and who is working on what topics. When I was starting one of my research projects as a student, I thought there were only handful of people working in this niche research area - as I continued doing my research and have attended a few conferences and presented my research, I figured that alone in my country there are dozens of researchers working on it. One of them is actually working just around the corner from my original faculty where I started my research!
Hence, asking the professors from your faculty whether they know somebody can be really helpful. And you can still ask your Prof. Wright, whether she'd like to support you.

You should establish in what capacity you are hoping for the professor to "advise me". You mention that you are open to collaborating on a project to mutual benefit; that can encompass a lot of things, including not-for-degree-credit and/or unpaid. You should consider what parameters you would find acceptable in your present circumstances. You should also consider how you can show the professor (briefly) what you have to offer.

If you are seeking for the professor to be involved in advising you for credit-bearing work at your own institution in a formal capacity, you should ask your course convenor or administrator about the procedures for appointing an external advisor/supervisor. It may not be a routine occurrence, but it does happen sometimes, for the reasons you have given, so explain that you have already corresponded with a professor about a specialist subject not covered at your own institution, and that you intend to approach her about acting as an external advisor/supervisor. Having ascertained your institution's procedures, you can then write to the professor asking if she would have the time to act as an external advisor/supervisor, giving a very brief outline of the credit requirements at your institution and its procedures for appointing an external advisor/supervisor.

You have already made clear that, quite reasonably, you are not prepared/able to travel to another continent at this time. However, it is possible that the professor has plans to visit your continent, so an in-person meeting may still be a possibility (although do not bank on this -- a professor is likely to have a busy schedule when travelling overseas, and may not be able to make time to see an undergraduate).

In order to avoid sounding demanding, I would include something to the effect of:

Your feedback to date has been very useful to me, and I am hoping to pursue a project in interrogating postnihilism, as part of my final-year coursework for my degree of Bachelor of Arts in Futile Studies. Unfortunately, there are no specialists in postnihilism at my institution, so I am in the process of looking for an external advisor/supervisor. The degree requirements are quite flexible, so it could be a collaborative project with the advisor/supervisor. Is that something you might be able to do, or, if not, do you know any other postnihilists who might be up for a remote collaboration with a very junior research assistant? Ideally, I would like to work with you, but I realise you may be too busy, and you have, of course, already been enormously generous and helpful with your responses to my various research enquiries to date.

I want to add an answer here that is as encouraging as possible, especially for undergraduates just initiating a (hopefully enduring) research career.

Yes, you can be advised by a professor who is far away. Yes, skype-style videoconferences and other online collaboration tools make this easier than ever. Sure, it will be more challenging in many ways than setting up the typical weekly research meeting with someone on your own campus, but if the topic area is one where you are really passionate and the professor is willing to commit to make it work, then you should absolutely give it a go!

Many senior researchers in non-lab STEM fields collaborate this way with colleagues for the entirety of their careers, and it is very rewarding and has led to important results in my field for sure. If possible, see if you can plan a trip or two in advance when you can meet together live. Lots of progress is often made on these trips, and they provide helpful deadlines that can be motivating!