Everyone in grad school has taken on the task of picking the perfect research group at some point.  Then some among us had the dubious distinction of choosing the perfect research group twice.  Luckily for me, a year of grad research taught me a lot and I found myself asking group members and PIs (primary investigators) very different questions.  And luckily for you, I wrote these questions down to share with future generations.  My background as an experimental applied physicist showed through initially, so I got Shaun Maguire and Spiros Michalakis to help make it applicable for theorists too, and most of them should be useful outside physics as well.

Questions to break that silence when your potential advisor asks “So, do you have any questions for me?”

1. Are you taking new students?
– 2a. if yes: How many are you looking to take?
– 2b. if no: Ask them about the department or other professors.  They’ve been there long enough to have opinions.  Alternatively, ask what kinds of questions they would suggest you ask other PIs
3. What is the procedure for joining the group?
4. (experimental) Would you have me TA?  (This is the nicest way I thought of to ask if a PI can fund you with a research assistance-ship (RA), though sometimes they just like you to TA their class.)
4. (theory) Funding routes will often be covered by question 3 since TAs are the dominant funding method for theory students, unlike for experimentalists. If relevant, you can follow up with: How does funding for your students normally work? Do you have funding for me?
5. Do new students work for/report to other grad students, post docs, or you directly?
6. How do you like students to arrange time to meet with you?
7. How often do you have group meetings?
8. How much would you like students to prepare for them?
9. Would you suggest I take any specific classes?
10. What makes someone a good fit for this group?

And then for the high bandwidth information transfer.  Grill the group members themselves, and try to ask more than one group member if you can.

1. How much do you prepare for meetings with PI?
2. How long until people lead their own project? – Equivalently, who’s working on what projects.
3. How much do people on different projects communicate? (only group meeting or every day)
4. Is the PI hands on (how often PI wants to meet with you)?
5. Is the PI accessible (how easily can you meet with the PI if you want to)?
6. What is the average time to graduation? (if it’s important to you personally)
7. Does the group/subgroup have any bonding activities?
8. Do you think I should join this group?
9. What are people’s backgrounds?
10. What makes someone a good fit for this group?

Hope that helps.  If you have any other suggested questions, be sure to leave them in the comments.