The most common answer, by a long, long, looooooong ways was, “I want students to have some idea of the research I do.” To give few examples:
Wrong = have no idea what my lab does.
I want someone who knows why they want to work in my lab.
Read some lab pubs before talking to PI.
Wrong: they don't know that my lab is computational. Right: they have checked some of my publications.
– Gabo MH
Do show up in my office having read a few of my publication abstracts (on my web site) with a specific possible interest.
Show that you have actually looked at my website and read some papers, and explain what skills you have that are aligned.
Prospective student claimed interest in my lab, then asked what I study & if I have pubs. Informed her about Pubmed.
This reflects a larger aspect of research culture: the expectation that people who want to join in research will read the literature. Of course, new people may not know what “the literature is,” thinking we mean Dickens, Chaucer, Homer, and the like. But we can explain that to them.
That said, back at a mentoring workshop I was participating in a while ago, when I told students that they should have an idea of what professors do, one student spoke up. “Isn’t it egotistical for you to say you’ll only work with students who will work on projects interesting to you?” I can’t remember my answer. I’m still struggling with this question. Research opportunities on any given campus are finite, and I do wonder how many people get turned away who might be able to make good contributions.
Photo by Thompson Rivers on Flickr; used under a Creative Commons license.