I am a physics undergrad, who is also interested in pure mathematics. I am not very sure what I want to pursue for my PhD. Though I have specific interests in each of the two, and also inter-linked interests, in general I am very confused. My question is it legally and practically allowed for you to chose a guide from another department different than that which you are affiliated to? If not, can someone from another department become a co-guide? In particular, I am looking for laws and practices in the US and Europe (may differ from country to country).
Answer
Yes.
At least in the US, it is quite common for PhD students enrolled in department X to be advised by faculty in department Y, either alone or with a co-advisor in department X. Off the top of my head, I can think of PhD students in my (computer science) department who are advised or co-advised by faculty in electrical engineering, mathematics, and industrial engineering. Similarly, faculty in my department who advise PhD students in mathematics, electrical engineering, mechanical engineering, and biology.
That said, if you enroll in the PhD program in department X, you will have to satisfy the degree requirements (courses, comprehensive/qualifying exams, etc.) for department X, even if your advisor and your eventual research interests are in department Y.
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