Question

This post asks for resources to handle the following situation: "I, suddenly, have students" and many wonderful answers have been provided. My question here is sort of a prequel: recently, a post-qualification second year graduate student $X$ expressed an interest in working with me.

What should I put $X$ through before agreeing to advise him or her?

I don't mean to ask about the part where I point $X$ to appropriate literature from my field and help $X$ to understand the textbooks and survey papers as needed: that I can do. But how should I measure $X$'s aptitude and gauge interest levels, etc? I don't want this to be a long and drawn out process for obvious reasons. The zoomed-out version of my question probably should be:

What do you look for in a graduate student before you agree to advise him or her?

If it turns out from the responses that this question is overly subjective and leads to wildly varying opinions, I can make the question community wiki.

Answer 1

I usually suggest the student spend a couple weeks, or more if they want, taking a look at a little bit of material in my area and then come talk more with me, so that we can both get a sense of whether the area is a good fit for the student. Typically, I print out a survey paper in my area and suggest the student start reading part of it; and I also ask the student to try to do a couple of exercises from a book in my area, suggesting the student pay attention while doing this both to whether the material seems to mesh well with the student's talents and also to whether they find it enjoyable/engaging. I find it very informative to see how this goes and to chat with the student after they've grappled a little with this material; I tell them I don't think either one of us should make a definite decision until after they do this. Of course I try to make it clear that it's fine to come back with questions about the material. This also buys me a little time to learn more about the student -- like Lee Mosher mentioned e.g. how they did in coursework.

Some of the students who have approached me seemed to think combinatorics (my area) would be the easy route through grad school, which I do not believe is true at all -- so I try to communicate that it's an area where on the one hand questions may sometimes have simple statements, but on the other hand may require a lot of ingenuity to solve. Based on this experience with students, I think it's also important to make sure students aren't making decisions based on misconceptions. So I second everything Lee said too.

Others here have surely had many more students than I've had so far, but I did have the experience of being approached by a large number of students right after starting a tenure track job, so gave this a lot of thought then.

Answer 2

To gauge aptitude you can look at how the student did on the qualifying exam or exams that are closest to your subject. To gauge interest you can see if the student has taken advantage of nearby seminars and conferences in your subject, and you can talk to the student about what they got out of those experiences.

Answer 3

I have a strong opinion on this topic: a potential advisor must have an excellent reason to refuse to advise a graduate student who meets certain minimal requirements. The department has accepted the student. Presumably the student has successfully passed prelim exams, etc. The department as a whole has promised to help the student in their pursuit of a PhD. In my opinion, it is inappropriate to tell a student that, although the department promised to help, I personally think you do not deserve / warrant my advice. There are obvious exceptions: too many current advisees, personality conflicts leading to unhealthy working relationship, etc. Agreeing to advise is not a guarantee that the student will make progress, and if they do not, both parties should re-evaluate the relationship. However, faculty have an obligation to the PhD candidates admitted to the program. They should accept advisees unless there is an excellent reason to refuse.

Answer 4

I have a strong opinion on this topic: a potential advisor must have an excellent reason to refuse to advise a graduate student who meets certain minimal requirements.

I have developed an equally strong opinion in the opposite direction: a graduate student should show his ability to surpass the so called "minimal requirements" by far and large to even start talking about my becoming his adviser. Unless you want to end up defending PhD yourself a second time with your tongue and hands disconnected from your body and operated by remote control, you'd better make the student undergo a few severe tests over an extended period of time. If he survives, he's worth trying. A good place to start is to give him a tough but self-contained paper in your field and ask him to read it within a month and present it to you.

I do not believe in any "promises" or "obligations" to graduate students. We give them an opportunity to learn and to prove themselves worthy, but that's about it.

Sorry for "being argumentative", but since we touched the moral grounds in this question, you should keep in mind that the moral standards vary a lot from place to place and from person to person, so I would hate having you swayed by Jason's argument without being aware that not everyone shares his point of view. In short, make your own choice on the matter. You have as clear head and keen eyes when evaluating a potential candidate as everyone else.