I have been contacting professors about openings in their lab for a PhD position. One professor who I really want to work with contacted me back immediately and told me he would turn over my info to senior lab members (CV, transcripts) and that they will then get in touch with me.
It has been 10 days since that correspondence, I have not heard from anyone else in that lab and I do not know the contact info for anyone specifically, i.e. the professor did not mention exactly who would be looking at my info (although on their lab webpage they do list post-docs and PhD students with contact info).
I would like some feedback about when and how one might contact the professor to check on the status. My thought is to reach out to the professor if I have not heard anything in 3 weeks. I would say something like "Hello Dr. Soandso, I really appreciate the opportunity to be considered for a spot in your lab. 3 weeks have past since our last correspondence, and I just want to check that I did not overlook any communication from the senior lab members you mentioned. Thank you very much for your time." I keen that 3 weeks is a good amount of time for a follow up email.