Advice to get new PhD opportunities

Question

I have a master's degree in Mathematics in a specialty X. I got a scholarship to do a PhD thesis in a specialty Y in another country. I have started working on my thesis and I have devoted most of my time to read books and articles in order to get familiar with the speciality Y and with the subject of my thesis. My relationship with my advisor was very bad, he was not supportive and he wanted me to quit my thesis in first year, since he was convinced that I couldn't succeed it. Four years later, I have finished my thesis (I did the work that my advisor told me to do), However he has refused to approve it. Now, I have quit this thesis and I want to get another chance to do a PhD thesis in the speciality Y because I have worked so hard for four years and I have gained a good research experience (even though I don't have publications).

I want to contact some professors to ask them for PhD opportunities in their lab, but I don't know how should I talk about this (negative) experience so that I can convince them to work with me ?

Answer 1

In the US, the concept of a "lab" for (pure) math is a bit foreign. You apply to a department and are evaluated by a committee. Advisor selection only comes later, often after you pass qualifying examinations.

There is no reason that you couldn't apply to a doctoral program in US in the normal way. You need good letters of recommendation to predict your success, though they might not come from your current advisor in this case.

You should also write a CV with a good "Work in Progress" section, listing the projects that you worked on up to now, including the work you have abandoned in the short term.

Point your Statement of Purpose at topic Y and emphasize that you have extensive experience in that area, which would be echoed in your CV.

Make a broad search. Make sure that any department that you apply to has one or more faculty specializing in Y (or related areas). If they have several, with an ongoing faculty/student seminar in Y then all the better. There is no need to contact individuals prior to applying, though you could ask a few people for an evaluation of your work. If they respond positively then your prospects are better, though many will not reply at all because of the admissions process here.

I would emphasize the positive in any application. Don't mention conflicts and things that might be seen as failures or disputes in any written materials.

The same might be true of Canada, but less true in some parts of Europe, especially Germany. In the US, funding is normally from the department, not an individual professor. And applied math will be a bit different, even in the US.