Potential Red Flag (on my side) in PhD Interview

Question

Before anything else, I want to mention that my field is mathematics. Recently, I had an interview for a Ph.D. program for a research group that consists of two fields, say X and Y. On the application, I indicated to work in the field of X. However, in my statement of purpose, I mentioned that recently I also got interested in the field of Y, though I don't have much experience in that field so far.

Due to the structure of the program, I have some time to pick an advisor in the program (slightly more than a semester). When I got asked whether I would like to do some more exploration before committing to a project, I mentioned that the program requires me to take courses on field Y in the first semester, and as I am interested in that field, I would like first to see whether I would like to switch my studies to the field of Y. There were only two professors on the interview, both were on the field X, so I am wondering if this can be seen as a potential red-flag that I am unfocused.

Answer 1

It seems to me that you are overthinking this. If a student wants to decide between X and Y and both X and Y are supported, then it is not a lack of focus to delay the decision until you learned enough about Y. A lack of focus would be wanting to do both and Z and A as well. You answered a honest question honestly.

Internally and not visibly to you, there might be all sorts of dynamics. If your answer were to get you rejected from the program, then to me that would be indicative of internal problems that are good to avoid. E.g. if only people in X want to take on students or if no other good candidate wants to work in X, then your answer would not be optimal, but then they should have asked you differently. That example would be some form of entrapment and if this were a game that played on you then you are better off outside of this program. However, few places are that dysfunctional. You should assume that their question was honest. From the perspective of an outside observer, your answer makes perfect sense and shows that you are honest in your interactions with your potential advisors. I personally would count that in your favor. At least, you did not contradict your statement of purpose.