Back in March, I put a paper (joint with Maks Radziwill) up in the arxiv. It was 101 pages long (unsurprisingly, given that it was the outcome of several years’ worth of work) and may be a little hard-going. In particular, some readers may have mistaken some minor points or technical innovations for the main point.
I’ve decided to write an informal exposition, aiming for clarity rather than for conceptual perfection. I am hosting it on my departmental webpage, since WordPress would seem to like to charge me a stiff fee for using mathjax (or any other plugin) to display mathematical notation.
Here is the first part: https://webusers.imj-prg.fr/~harald.helfgott/Expansion_1.html