Advice about job applications in the US (mathematics) I did my Phd in mathematics in Europe and am at the end of my second year of postdoc in Europe too. I plan to apply for jobs in the US in the fall (ideally tenure track, but I wouldn't mind too much doing a second postdoc, as I finished my phd early). I think it's the best place for me, as most of the researchers in my field are in the US. But I'm not familiar with the american system at all, so I would be happy if you could help me answer a few questions:


I know most applications go through mathjobs.org and that there are hundreds of applications for a every position. What is the best technique for an application not to be overlooked? Is it common in the US to email a professor at the university which offers the job and let them know that you applied/tell them that you would like to work with them? If yes, is it even ok to email a professor that I don't know personnaly but who I think knows my work or would be interested in it? In Europe it is very common and even necessary, at least in the countries I know, but I wouldn't want to do something that is weird or unethical in the US.
Someone told me that US universities tend to favor people who are already working in the US, especially for tenure-track positions (something about not wanting to pay a flight from overseas for the interviews). Is that true? Is it the same for postdocs?
Is it weird to apply for both a tenure-track position and a postdoc position at the same university? If I did so, would they automatically think that they'd rather give me the postdoc as I'm ok with both, and give the tenure-track to someone who applied only to tenure-track?
Are the chances of getting hired in an university where no one works on the same things as I do very low? Of course I would prefer to be in an university with nice collaboration opportunities, but just in case I was thinking of applying to others too.


Thank you very much in advance for your replies!
Answers to your questions (the numbering is the order you asked them):


You should definitely email people at the university who might be interested in and familiar with your work.  But for tenure track positions it is weird to say you want to work with them.  Instead, I would just send a low-key email just letting them know that you applied to their position and would be very interested in coming there.  The goal is to be informative but not pushy.
It is true that it is both more expensive and more difficult logistically to interview someone who is coming from overseas, but it certainly does happen.  They just have to want you enough.  For postdocs, there generally isn't an interview, so it isn't an issue.  However, some kinds of postdocs are funded by sources like the NSF that only want to support US citizens or permanent residents, so foreign applicants won't be considered for them.
It's not weird at all.  Doing so will not affect your chances at getting a tenure-track position.  Everyone knows that the job market is tight.  
There has to be someone at the university who advocates for hiring you, which means at least they appreciate the kinds of math you do.  But certainly there does not have to be someone who works in precisely the same part of mathematics (and in fact often the "needs of the department" involve hiring in fields that are not well-represented there).


My background: I've served on a large number of search committees in pure mathematics at a couple of different private research universities.