Do American-educated mathematics PhDs generally have an advantage over natively educated PhDs (in, say, France or Italy) in applying for research positions?

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    What gives you the idea that they do? – Sumyrda - Reinstate Monica Dec 10 '15 at 4:49
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    @Sumyrda, I don't know whether they do or not. I'm interested in the question because it's always been a dream of mine to research abroad. – Danny Dec 10 '15 at 8:01
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    What is "mainland Europe"? Why exclude the islands? Do you have cause to believe PhD's from the USA are viewed differently in Corsica, for example? – user9646 Dec 10 '15 at 10:19
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    @NajibIdrissi "mainland Europe" means to exclude the UK. In many ways the UK share some similarities with the US whereas the "mainland" countries do not – Cape Code Dec 10 '15 at 13:01
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    I suspect that "mainland Europe" excludes Ireland too. – Shane O Rourke Dec 10 '15 at 23:45

Do American-educated mathematics PhDs generally have an advantage over natively educated PhDs (in, say, France or Italy) in applying for research positions?

Generally speaking, no: why should they? And for what concerns specifically Italy, take into account that some things that can make an application strong(er) in the US (e.g. stellar recommendation letters or awards), might go totally ignored by a selection committee in Italy. This means that you should tailor your application to the country you're applying to. Let's see why.

A selection process in Italy, both for permanent and non-permanent positions, is usually composed of one to three steps, where each step counts for a fraction of the final mark (details vary across fields and position levels):

  1. CV and publications (this step can count from roughly 30% to 100% of the final mark). The selection committee, before knowing the candidates, decides how to evaluate each section of the CV. If, e.g., the call doesn't explicitly mention recommendation letters, these are typically discarded; if the committee decides that awards count at most 2 points out of, say, 30, even if you have a Nobel prize, they (probably) won't add more than two points (should they do, in case of appeal from some of the candidates, the call can be invalidated).
  2. One or two technical essays (optional; when present can count from roughly 30% to 50% of the final mark). Here, the applicants are typically required to write a technical essay on a specific topic in the field of the call. I don't know about mathematics, but in my field one might be required to describe how a certain instrument works (e.g. a spectrum analyzer) or how to perform a certain experiment (e.g. how to measure the fine structure constant). The difficulty of the question depends on the level of the position.
  3. Interview (optional, depending on the position). Here the applicants are typically asked to discuss technical topics in their field or, for instance, some of their publications. For an associate- or full-professor position, this step can be substituted by a (public) lecture on a specific topic in front of the selection committee.

I don't know about mathematics specifically, but in general the Italian academic market is very difficult to get into. There are a lot of budget cuts, so there are few positions available. Moreover, it helps to have a local network, if only to find out which positions are available. That puts foreigners at a disadvantage.

This is not to say that you should give up your dream, but only to warn you that it is not going to be easy.

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    This answer is good just for Italy. And maybe Spain. But It has absolutely nothing to do with having an American PhD , but with the fact that these countries have a very closed and "old-school" academic systems, where funding is scarce and outsiders are not as positively seen. The information you have shared is partial and has not much to do with the origin of the PhD, and that what the OP is asking about. This shoudl be a comment maybe. – Ander Biguri Apr 29 '16 at 10:15

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