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I am masters student and I am applying for phd position in analytic number theory in Europe. But there are very less number of professors in analytic number theory as compared to algebraic number theory. Also some professors to which I wrote didn't even replied.

Recently I was watching a lecture of a professor of India whose name is Ritabrata Munshi (ISI Kolkata) who works in analytic number theory, he mentioned in interview his phd guide was Andrew Wiles who he mentions as an algebraic person. Then professor Ritabrata munshi mentions prof Andrew Wiles didn't changed him to an algebraic person and Ritabrata munshi works even now in algebraic number theory.

So, my question is, should I apply to professors working in Europe in algebraic number theory for working for my phd thesis in analytic number theory OR

I should consider this case as an exceptional case as Andrew Wiles is one of legendary persons in Mathematical Community and I as I was searching about Prof Ritabrata munshi , he has also made great contributions to analytic number theory and I should also remember how good in Mathematics Ritabrata Munshi must be as Wiles agreed to guide him for phd at Princeton University!!

So, is applying to professors working in algebraic number theory for phd in analytic number theory right or wrong?

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    Surely there's no real answer to this question. Certainly there are algebraic number theorists that use enough analytic number theory as part of their research that they'd likely be fine supervising a thesis that was quite analytic. But there will also be many others whose research is further removed from analytic number theory and who would be uncomfortable supervising an analytic thesis. – user109454 Dec 19 '19 at 15:28
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Let me give some advice that depends very little on your field and on the differences between approaches to number theory.

Perhaps you can find the ideal advisor to continue your current trajectory. But perhaps you can, instead, find someone else who will be less than perfect, but still permit you to advance your career. A relationship between a student and an advisor is a mutual one. Often the student has to bend their trajectory a bit so as to find a good match.

But you don't have to adopt a new trajectory forever. Once you prove yourself as a mathematician you can choose which path to follow. Perhaps you will even learn something about your main preference by working in a (fairly) closely related subfield.

The suggestion, then, is to find an advisor who wants to work with you and who has sufficient background and flexibility to guide you well and set you off on a career. In particular, don't aim too narrowly so early in your academic career.

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  • you are right that I should not be so narrow so early in my career. But I have only studied analytic number theory and I don't have any idea about algebraic number theory. Although, I know considerable amount of analytic number theory but all of it I have studied by myself, my university doesn't run good amount of courses in pure mathematics. So, I had no option except that of self stuying and I could not devote time to algebraic number theory as I also have to pass applied maths courses despite not liking those courses. – Yannic Muller Dec 19 '19 at 15:54

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