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As the title says, how common is it for mathematics departments (in the US) to notify postdoc applicants when they're shortlisted?

As I'm currently waiting for postdoc offers and haven't got any shortlist notification yet, I want to know if I should start to panic.

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Regarding whether you should panic, the answer is no, but see here for advice about what to do at different times in this process. – Anonymous Mathematician Jan 18 at 22:47
    
Shortlist notices usually happen in the UK, but the converse does not hold - if you are not shortlisted, do not expect to be contacted. – Captain Emacs Jan 21 at 11:11

It's not common to officially notify applicants that they are on a short list. If you find out, it will probably be via backchannel communications through your advisor. That's the best way to gather information, since your advisor's contacts may be more open with him/her than they would be with you, and your advisor can put in a good word for you at the same time.

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Anecdotally, I received two short list notifications directly from search committees, one of which eventually made me an offer. I suppose I may have been on more short lists. My advisor didn't spill any beans to me, but I think he knew more than he let on, since when I told him about the offer, he already knew. (This was only a few years ago.) – user37208 Jan 18 at 22:57

My experience on the postdoc market this year suggests that, contrary to the answer above, shortlist notifications are in fact pretty common. I received several official notifications in the last 10 days or so, informing me that I was on the shortlist for postdocs at major universities. My advisor was not involved at all. In a few of these cases, offers came shortly after I indicated I was still interested. So I think the phenomenon is real, and my guess would be that it is largely done so that the universities can gauge the applicant's interest. My semi-educated guess would be that only people towards the top of the shortlist are notified, and that the phrase "you are on our shortlist" is a euphemism for "an offer may well be coming soon".

You should absolutely not panic though! For one thing, I think many people are sitting on several offers and mulling their options (e.g. I was for a week until I accepted an offer recently). Many of these will be released again soon when the applicants with offers make their decision. Secondly, I think that the NSF postdocs will be finalized on Friday (the 22nd), and I gather that many universities are waiting until this date to release offers. Further, even if you hear nothing next week, do not worry. A friend of mine heard absolutely nothing until Feb when he was a postdoc a few years ago. He ended up getting (and accepting) an offer at a top 10 school.

This is all just my anecdotal experience, so take it with a grain of salt.

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That's funny. My sources had told me that the NSF postdocs were sorted out last Friday. Have you applied and not received a decision? – Ben Webster Jan 21 at 15:37
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I applied from outside the US and am ineligible for NSF funding. I got the 22nd of Jan date from the AMS webpage on the common deadline. If someone can confirm that the NSF offers have in fact been sent out I will edit my answer. – faisceaux Jan 21 at 16:32

I propose a resolution of the two answers given so far. I think top institutions which make postdoc offers in a timely manner generally have little reason to contact people on the shortlist, as they'll have a relatively high chance of acceptance.

Other schools that make postdoc offers later, particularly in the case of candidates who are also on the tenure-track market (where the timeline is earlier), might send out feelers to candidates at the top of their short list to see if they are still available and perhaps gauge how interested they are. This often helps make the ordering of the short list easier, once some candidates can be omitted or deemed unlikely to accept. It also speeds up the process as once you make an offer you may need to wait a couple of weeks, get rejected, and need to start over, by which point other candidates you like may be off the table.

Our department does this at least some of the time, and occasionally I will personally contact a candidate I'm interested in (even when I'm not on the search committee) to see if they're still interested. If I know they are likely to accept, it makes it easier for me to push for this candidate, especially when we have to make late offers.

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