I'm about to apply for postdoc positions in the US through mathjobs. I already did it last year, so I have my reference letters from the previous time (which are probably pretty good).
Now here's my situation: During the last year, I was lucky to solve some well-known open problems in my field (well, it's not going to earn me a Wikipedia entry, but the tiny group of researchers in my esoteric field is impressed), which will probably turn my application from "good" to "outstanding". In order to really make my application look better, my reference letters should address the recent results, so I asked my letter writers to update their letters. Most of them did so, except for one (who didn't reply to my emails). The problem is that I should submit some of my applications by November 1, and as I didn't hear from that letter writer for several weeks now, I'm afraid that he might not update his letter by November 1.
Question 1: When job ads on mathjobs say something like "screening of applications will begin on November 1", do they really mean it, or do they mean something like "screening of applications will begin on mid December, but we want you to submit your application early"?
Question 2: What would you do in my situation (assuming that the relevant letter writer is currently abroad and I have no other way to contact him)? Should I contact the relevant search committees and ask them to check that reference letter a bit later, once it gets updated?
Question 3: If a letter of recommendation is updated on mathjobs past the submission of an application, which version of the letters is available to the search committee? What should I do in order to make sure that they read the updated version?