This short post is in response to Jozsef Solymosi’s request for a new DHJ thread, since the previous one has become rather long and unwieldy. We’ve stopped numbering comments now, and the main purpose of the post is so that people can continue the discussion of the write-up of the proof of DHJ(k). Thanks mostly to the efforts of Ryan O’Donnell, we now have a complete draft. See also this write-up of DHJ(3) by Jozsef.
While I’m writing, I thought I’d take the opportunity to say that I am not intending to post much over the next two or three months, either here on on the Tricki. That’s because I have three more or less completed research projects that need to be properly finished (one of which is DHJ) and I owe it to my coauthors to get them done. So the plan is to clear my backlog over the summer and then come back, refreshed and ready to go, in the autumn. At that point I plan several Tricki articles (more advanced than most of the ones I’ve written so far). I also plan to start a new polymath project. Or rather, I have a file in which I have written plans for ten polymath projects, so what I’ll probably do is explain briefly what they are and try to get some idea of what appeals to people most. I am excited about several of these possible projects, so whatever we do I will be disappointed about the ones we don’t do. I may well have an online vote about it, but first I have to decide what the results of the vote will be.