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Thanks a lot for the replies! It helped a lot.

Hi, So the situation is, I was invited to the interview by a faculty that I wrote on my personal statement as a second-choice mentor. It was surprising considering that I only contacted the first-choice mentor and spent several sentences on PS why we would be a great fit, but only less a sentence on a second-choice mentor. Anyway, I'm very grateful and super-excited to be there because this university was one of my top choices. However, I am concerned about what to say and what to ask the first-choice mentor on PS. Actually, I experienced this same situation last time. Last year, I was invited to the interview by a new professor who was not on the webpage yet. Although the fit was amazingly great (we had almost exactly the same research interests), I was somewhat disappointed because the professor I wanted to be my mentor was a so-called "big guy" in my field and did so many amazing research. In contrast, the professor who invited me was just out of grad school and had no grants. I know I shouldn't have shown this disappointment in my interview, but I was so nervous and stupid that I made so many terrible mistakes. For example, when I was asked about the research ideas by the professor who invited me, I told to the professor that with this and this idea, we could collaborate with the professor X (the big one), and I felt that you guys' interests overlap a lot, blah blah blah... Yes, a whole nightmare... I still hit my head to a wall when I'm reminded of this. Of course, I was rejected, and that was the only interview I had. So, I had to start all over again this year, and I don't, NEVER, want to repeat the same mistake. So, now I know what I should not do, but I still don't know what to do. It is possible that I will not be matched up with that professor, but probably will be because of our shared interests and we will meet in other socializing settings throughout the interview days. I'm aware that I should show my deep gratitude and interests to the faculty who invited me, and I'm preparing that. In addition to that, I would appreciate your ideas and suggestions on what questions I should throw to the first-choice faculty or the stance I should take while I'm talking to the faculty, etc. Thanks a lot!