Should major awards be included in an NSF postdoc application? If so where? I am applying to the NSF postdoctoral fellowship in mathematics. As I understand it, I am essentially trying to convince the NSF that my proposed work is interesting, and that I am able to do it. In service of the second point, it seems like I should point out major professional awards (departmental awards, for instance). This information would appear in my cv for a job application, but the closest document for the NSF application is the biographical sketch, which has strict requirements on its contents.

Should major awards appear in my nsf application? If so, where?

Parenthetically, same question regarding invited talks (although this one is explicitly ruled out as part of the bio sketch)
I think that you should follow the NSF's application instructions to the letter and not include any information that has not been asked for. In particular you should not add any sections to the Biographical Sketch beyond what appears in the NSF Proposal &amp; Award Policies &amp; Procedures Guide. This guide explicitly states, by the way, that "Inclusion of additional information beyond that specified below may result in the proposal being returned without review."

As you state, you need to convince the NSF that the work you are proposing is interesting and that you can actually complete it. For the former, this is what your Project Summary and Project Description are for. As for the latter, your best argument will be to rely on your previous work. You'll be able to list some of your publications in the Biographical Sketch, and can mention your previous work more explicitly in your Project Description. 

Finally, if you really think that it will help to point out departmental awards, invited lectures and whatnot (and it is far from clear to me that this will help you all that much), you can always ask your letter writers to include this information in their letters.