To begin with, I must point out two things: first, to read this post faster, you can skip directly to the questions and the paragraph before them; second, although I mention a specific field of mathematics, I think the question is quite general and applicable to any field.
I am currently a master's student in mathematical logic. A year and a half ago I finished my studies in physics and the following year I studied a master's degree in mathematical research (the courses were on pure maths like algebraic geometry, functional analysis, differential geometry...). But for a few years my interest has been in mathematical logic, that's why I enrolled in this master's degree in logic.
During this course I have reached two conclusions: I have found the specific area of logic that interests me (model theory) and I have realized that I am close to a burnout. have learned a lot, but the pressure from the exams and the heavy workload in areas that do not interest me or that have not been very well taught (I allow myself to make this complaint because I do not consider that it is the fault of the teachers, but of a very improvable study plan) have made me rethink my plans. In particular, my intention is to try to jump right into a PhD, since I like to study a lot, but I need more freedom to work.
During my previous bachelor's degree (on physics) and in my previous master (on pure math) I got good results (grades of ~9/10 average) and my intention is to finish only a few subjects of my current master (on logic). However, I don't know if that will be enough to get me into a PhD. I have asked for advice from one of my professors, who is a well-known expert in a field not too distant from the one that interests me (model theory) and he has told me that without any problem I can ask some suitable experts in this area if they would be willing directing my PhD, but I don't know if I really have a chance of getting a positive response and I'm not sure if it's a good idea without knowing the chances of success I have.
All in all, my doubts are:
- With my background (which I mentioned at the beginning of the previous paragraph), can it be very difficult to get a PhD and funding (even if it's little) at a decent university in Europe? I would like a PhD in the European Union and as close as possible to Spain (which is where I have studied).
- Second, if the above is difficult, is it preferable to do the PhD in a nearby area that interests me but with more professors and, after the PhD, try to get closer to the area that currently interests me more?
- Finally, if I spend a year studying on my own and trying to get small results that could be the start of a PhD, would that benefit me when looking for a advisor or is it bad for my CV to spend a year without increasing it?
Thanks in advance!!