I was hoping to get some opinions on my current situation involving leaving one advisor for another.
Background: I am a second year graduate student in applied mathematics and I have passed all my qualifying exams. In my first year, Distinguished Prof. K reached out to me and I began doing research with him. Prof. K is very well known in his sub-field of applied math. In the past year or so, Prof. K has helped me apply for two large fellowship awards (I don't know if I will get them or not yet) and we have met once a week for about 15-20 minutes. My concern is that when we are meeting, Prof. K doesn't doesn't help really at all on the math side of things and he is often distracted by emails/phone calls which interrupt our already short meetings. In short, he has become extremely difficult to work with and I don't feel like I have accomplished much mathematically.
Last semester, I took a class in numerical PDEs from a younger professor, Prof. N, at my university. I really loved the course and reached out to him about doing a research project last October. Prof. N is definitely one of the smartest people I have ever met. We meet once a week for a full hour and he is completely focused on helping me further the mathematics of the project. I asked Prof. N last week if he would be willing to be my advisor and he said he would be happy to. I cannot stress how much better the whole experience has been with Prof N. I really feel like he can help be really successful in my thesis.
A few notes: - Prof. N and Prof. K are in very different sub-fields of applied math. - Prof. K doesn't know about my work with Prof. N yet. - Prof. N has offered to reach out to Prof. K for a joint project if I want.
At this point I am fairly certain that working with Prof. N would be better for me and my career. I really feel like I can be more successful with Prof. N in numerical analysis than I can be with Prof. K. I actually question a bit whether or not I could finish the PhD with Prof K at all because I receive almost no math guidance or help.
1) Is the prestige of an advisor super important? Prof. N is definitely a much better advisor for me and, in my opinion, much better at mathematics than Prof. K but Prof N is not as far along in his career. I am wanting to make sure I can get a post doc position after I graduate without a super prestigious advisor.
2) Should I consider the joint project? My first instinct is that I definitely don't want to do that because I want to focus in the area of Prof. N and learn as much as I can from him. Prof K is just really difficult to work with and I am worried that joint collaboration with Prof K will just ruin the currently perfect project I have going with Prof. N. There is also some possible tension between Profs. K and N (all due to Prof K) that I am aware of and don't want to create a problem (I am not even sure if Prof. N is aware of this possible tension). I am sure they could both be professional if we were to collaborate though.
3) I really feel that I need to tell Prof. K about my work with Prof N at this point and I am really struggling with how to do this. My first instinct is to do it in person; however, I struggle to finish thoughts in meetings because of interruptions by Prof K. Because of this, I was considering writing him an email and then talking in person if need be. Either way, I will of course be very grateful and professional in the way I do it.
Thank you very much for your thoughts and input. Please let me know if you have any questions for me.