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I'm submitting postdoctoral applications to a few places to receive external grants, and I've written a proposal all by myself. However, I'm planning to come back to academia after two years in industry that didn't go very well, and also my postdoc application subject (statistical machine learning) is significantly different from my PhD thesis topic (differential geometry and low dimensional topology) and also I was forced to divide my time in the US and Europe (in Europe now and planning to stay that way), so I'm feeling academically isolated and I'm not fully confident that the research proposal will generate interests.

So I think if I can contact a faculty member who works in the relevant directions, (s)he takes a look and gives me her/his honest opinion, I'll benefit a lot from it. However, since I'm academically isolated because of the reasons mentioned above, my only chance to write to a faculty who could be kind enough to take a look. Just to make sure, I'm not planning to work with her/him directly - I would if I could but geographical constraints prevent me. So will it be strange or impolite to try my luck this way? And what will be the best way I can write my email and its subject to make sure (s)he takes a look?

P.S. As mentioned in comments, no, my PhD advisor can't do anything here, even though he's a very accomplished pure mathematician, and I've all the respect for him.

P.P.S. The real problem is: I don't know people in person who do research in this topic.

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    Contacting people who know you is much more likely to be productive than contacting those who don't.
    – Buffy
    Dec 1, 2020 at 12:07
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    Perhaps your PhD supervisor would be a good place to start? even if the topic is unrelated they can likely give you good advice about the overall structure and general content.
    – astronat
    Dec 1, 2020 at 12:08
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    @astronat, good idea. They may also be able to point the OP to someone who might help and even initiate the contact.
    – Buffy
    Dec 1, 2020 at 13:56
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    The way out of isolation is through people you know. I really don't understand why you are discounting your advisor or other faculty members you have interacted with in favor of cold emailing people.
    – Jon Custer
    Dec 1, 2020 at 14:48
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    If your proposal directly references someone's paper, and it's clear that you have read it, mastered it, and suggest plausible ideas on how to extend it, then if you're lucky you might get a response from that person. But keep in mind that there is no way to "make sure (s)he takes a look"; the same rule of etiquette that says its okay to email strangers also says that it's not obligatory to respond. Good luck.
    – academic
    Dec 1, 2020 at 16:10

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When I was writing my grant proposal I was advised by professors to do exactly what you are describing, worst case scenario they're busy and they ignore you but it is not unpolite to ask.

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