I recently contacted a potential PhD supervisor expressing my interest in working with him. I attached all application materials (personal statement, CV, etc), as he requested on his website. I received a prompt reply that he is accepting graduate students for the upcoming semester and to let him know if I have any questions. How should I follow up with him, and what sort of questions are appropriate to ask at this stage? I submitted my formal application to the program soon after receiving his reply.
Ask for a phone/skype call to discuss research interests, and to see if the two of you would be a good fit.
Hi Prof X., Would you be available for a phone/skype call next week to discuss research projects and to see if I would be a good fit to be your advisee? Thank you!
As suggested by @Austin Henley, take a personal approach (phone/Skype is best). PIs want people who are passionate and who fit well. Plus, a bit of ego stroking never hurts. The candidate who takes initiative to call/Skype demonstrates interest and initiative, and a little bit of ego-stroking that can pay dividends. At that point, you become a person, not a piece of paper.