Hi Andrius, I'm skeptical here, though I don't exactly know what you have in mind. This is intended to be a workbook, with stuff that come up in practice for math-based study groups. Especially: when reading papers, there are lots of definitions to be hashed out. And then along with that there are examples of the definitions, theorems that say things about the definitions, proofs. Plus expository material which attempt to give the reader guided tours through the contents of the book. I.e. tutorials, possibly in a blog style.
So it's a group "math textbook," which can be fleshed out with exercises too.
It should be objective, and its contents potentially citable as a source of reference material.
So I wouldn't want to stretch it out, or dilute this focus, to include research projects, which it seems to be what you are hinting at. Of course that's important, but it's a very different gestalt. Relatedly, note that the wikipedia guidelines assert that original research doesn't fit into the encyclopedia genre.
In a sense there is more "personality" or subjectivity involved in research writings -- as one is trying to prosecute a thesis (similar considerations apply to philosophical works). The objective tenor of a math book just doesn't mix with this other kind of material.
We had begun a discussion contemplating how research projects might be "hosted" at Azimuth. It's a delicate matter. All else being equal this would be a good thing. On the other hand, I don't want to be hosting things at Azimuth which are too far out there. There's not cut and dried boundary line between these things, it's a contextual judgement call, which could be informed by our consensus based discussion process.
Sidenote: There is a further complication here, which is that our consensus based process is limited by the small number of currently active participants. Oh well, we have to work with what we have - and hope that it may grow as social circumstances evolve.
But in any case, one can always publish there research or investigations right on this forum. Look how well Paul has done that -- using just a single, long discussion thread, for an in-depth investigation of QBO and ENSO.
And as a reminder, everyone is encouraged to encouraged to create a personal page on the main wiki, and put it in category member. That page could contain an organized index of one's writings on the forum.
When I get more organized, I plan to do this for myself. The forum is a powerful medium; if you think about it, a single discussion can function as an entire "mini-blog," e.g., Paul's thread.
Note if any of these blog-like discussions turn out to be truly expository articles about math concepts, then that could potentially be included as blog-like tutorials in the mathbook.