I am a master's student who does a significant amount of independent research and is planning to apply for a PhD in mathematics at another university.
One issue I'm running into is that I already have a fairly well-developed research program that I would like to continue during a PhD. At the same time, I had the misfortune of becoming interested in areas that have become quite niche, making it difficult to find potential supervisors whose work overlaps closely enough with mine.
This made me wonder how common it is for a professor to supervise a PhD student who is largely autonomous and whose research lies outside the professor's main area of expertise, as well as how to find one.
Has anyone had a similar experience, either as a student or as a supervisor? I'd be very interested to hear about similar cases or experiences.