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I've just went through the 1st year of my PhD in France, it is related to Floer Homology. I didn't know what it was really about at that time, I chosed this subject because I thought it would combine all the stuff I love (different facets of differential geometry, algebraic topology, functional analysis...) but I kind of regret this choice now : I may like to learn and discover such complex and in the same time beautiful theories, I don't feel like building them, to sum up, I'm a bit fed up with all the abstract nonsense ...

On the other way, I had to teach a basic course in graph theory, a topic I never had met before. I really fell in love with it, since then, I spent my time reading stuff about graph theory and now I would like to change my plans, I didn't get any useful answers on french forums so I'll try here : -Is there a way, in France or abroad, to switch from my ongoing thesis to a PhD in graph theory? If not, is there a (not too long) bridge between these two?

I know a lot of you are going to think that I'm just avoiding difficulty and that I'll fall into it again when reaching a higher level in graph theory but I've already went through with that question and I'd appreciate only answers really related to my question.

Thanx you all for the attention!

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closed as primarily opinion-based by Nate Eldredge, Alexey Ustinov, Qiaochu Yuan, Franz Lemmermeyer, Ryan Budney Jun 21 '16 at 5:14

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ This question may be contingent on the nature of French (or Continental) academia, which many readers (including myself) may be unfamiliar with. In principle I wouldn't see anything wrong with the transition, but time may be an issue. I'm not sure I understand what you mean by "bridge", because to me it sounds more like a clean break and starting all over with a new adviser. $\endgroup$ – Todd Trimble Jun 21 '16 at 1:31
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    $\begingroup$ Caution: In many fields, the introductory level material has a much different flavor from the research level. The material you would cover in an introductory class is usually classical, well developed, and selected because it is particularly accessible and/or beautiful. The cutting edge is often much more frustrating and less pretty. So on the basis of teaching an introductory class, I would not jump to the conclusion that you will enjoy research in that area. Maybe try to pick up a side research project in that area before making any permanent decisions. $\endgroup$ – Nate Eldredge Jun 21 '16 at 1:51
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    $\begingroup$ Maaaybe. A lot of graph theory is pretty impractical. Conversely, if you were to just shift your focus a little, I'm sure you could find some very applied problems in geometric PDE, or some such area, that would let you take advantage of the expertise you already have, instead of starting from scratch. $\endgroup$ – Nate Eldredge Jun 21 '16 at 2:02
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    $\begingroup$ Well, this is the sort of thing that's best discussed in person, with people who know you, your abilities, and your priorities. It's not always so helpful to get advice from total strangers. And anyway MO really isn't the place to get it - we really want to keep this site focused on math content, rather than personal career issues. $\endgroup$ – Nate Eldredge Jun 21 '16 at 2:05
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    $\begingroup$ Calling graph theory "applied mathematics" is the weirdest thing to me. It is part of combinatorics, which is part of pure mathematics. At any rate, there are lots of graduate schools outside France, in fact most graduate schools are outside France. $\endgroup$ – GH from MO Jun 21 '16 at 3:07
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In the United States one usually spends 4-6 years in graduate school, and switching subjects and thesis advisors is quite common. In fact it is customary to start working on the actual thesis after the first or second year in graduate school. In Europe, switching is harder because the time in graduate school is usually limited to 3 years, and departments also tend to be smaller. What is worse, one has to choose a topic and sometimes even a thesis title before actually starting the graduate studies.

I don't think that graph theory is any closer to Floer homology than any other subject in mathematics. On the other hand, 2 years might be enough for you to write a thesis in graph theory, especially if you find an advisor who can guide you well. Another option that I recommend you to consider seriously: apply to graduate school again and start all over from scratch. It is definitely better "losing 1-2 years" at this point of your career than becoming a frustrated and miserable mathematician for a longer period (perhaps for life). Whatever you work on as a graduate student will have a huge effect on your later professional life.

Finally, a personal remark: I did switch subject and school during my graduate studies, and I have not regretted it (although many have advised me against it at that time).

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  • $\begingroup$ What you're saying is even truer in France, for instance I think it would be more difficult for me to move from symplectic geometry to riemannian geometry than it would for an US graduate to move from algebraic geometry to statistics (I may exaggerate a little, but you see my point ...). I fear that, in France, if I drop the thesis after one year, I won't be able to be funded to do another one after 1 or 2 years studying graph, I fear to be seen as "dropped_his_thesis_guy"... Furthermore, I also can't afford studying abroad without funding for 2 years... $\endgroup$ – spirz Jun 21 '16 at 1:49
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    $\begingroup$ @spirz: Most US (Canadian, British, German etc.) graduate students are funded by their universities, departments, advisors etc. Just apply to some US school, and you will have 4-6 years to work in peace on whatever you like (with funding of course). Usually there is no point in rushing the PhD degree, it is more important that you learn what you want and need to learn. $\endgroup$ – GH from MO Jun 21 '16 at 3:11

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