I interviewed with Yale this past Friday and had an independent meeting yesterday with the Professor I hope to work with. Didn't apply to Stanford so not sure about that...
I think it went well! It ended up being with two faculty members and they asked the standard questions and some more specific ones regarding my research. I'm not sure though what their timeline is, slipped my mind to ask at the end ?
I got an email from Williams today with an offer of acceptance to their program. I interviewed last Monday, and heard from the program admin that they would not be doing any more interviews after March 9th.