Hello everybody.


I am a Ph.D student in North America looking for advice about my prospective research area.


My supervisor works in a research area, let's say area A, so as soon as I was accepted as his student I started to learn the background in the area A. At some point I started to study by my own the connection of area A with a nearby area, let's say area B. I found that area B match much better my interest, I can use my former background in area B and definitely I have more mathematical intuition in that area. 


I have spent the last six months studying really hard several advances books, recent papers and lectures notes to get the necessary advanced background to start doing research in area B. Some days ago I had a meeting with my supervisor, I was really enthusiastic explaining the connection of area B with what he does in his research (area A), however my supervisor told me that it is not a good idea to continue working in that direction because it is difficult to be accepted in the circle of people who work in area B (several professors at top U.S. universities and their former/current students), that there is a lot competition between them to publish results and because neither my supervisor nor me belong to that circle it would be difficult to publish or even find a specific problem for my research.


I did not understand what my supervisor means when he said " it is difficult to be accepted in the circle of people who work in area B", does that mean that if I submit a paper it would not be published even if it is correct, well-written and meets the standard of quality and originality of the journal? or if I try to submit a talk to a conference in that area my talk would be always rejected?


I find difficult to believe that there are areas of mathematics that are closed to people who does not belong to a certain circle of leading researchers and their students. 


Despite this, I consider that is possible to perform my research in area B, I could contact by email people working in that area, several of them posed open questions and further directions of research in recent papers, moreover at the end of this year I plan to attend an important conference specialized in area B, a lot of junior and senior researchers of "the circle" are attending and I am interested and familiarized with the research of several of them, so the connections I could make there would be very useful. 


To sum up my questions are:


i) Is is true that there are areas of mathematics that are closed to people who does not belong to a certain group of professors and students at certain universities?


ii) If I make the right connections with people working in area B, do you think is feasible to perform my Ph.D research in area B with my supervisor, whose research is just nearby area B, and the advice of a specialist in area B mainly by email?


Some additional information: I am not very far from those universities where the people of "the circle" are, so I could travel from time to time to those universities to meet those people or give talks at the seminars. 


Thanks for your answers.



 Research topics restricted to students at top universities?  
Perhaps your advisor had meant merely that the group who work in area B are very strong and have a rich knowledge, and it is difficult for outsiders to enter into or compete with that group because they won't have risen to the high expertise to which that group had brought itself? You seem to present the issue as one of political intrigue and exclusion, but it may not be like this at all. There are surely many mathematical groups, who by working intensely on a focused topic bring themselves to a high level of expertise on that topic. If this is the situation, then it would seem by your other remarks that you can make contacts with that group and begin to study with them and thereby involve yourself in their expertise. 


That said, I also believe that it is wise to listen to one's advisor's suggestions about topics of investigation. It may be that your advisor simply feels that he will not be able to help you as much in area B, simply because he doesn't himself have the knowledge necessary to guide you in that area. Thus, your plan to work in area B is essentially amounting to not working with your current advisor, and instead having only an email advisor, who may not ultimately give you the attention that you will want and need later on, and that may not be the best situation. But if there is someone in that group who can server as your mentor, then it may work out.


Regarding questions (i), I think this kind of concern is likely misplaced. In my experience, any mathematician with talent will eventually be recognized for it, regardless of whatever connections they may or may not have.


