Decoupling, efficient congruencing and Vinogradov's main theorem It seems to be word in the generic corridor that decoupling (as in Bourgain-Demeter-Guth) and efficient congruencing (Wooley) are deeply related, and even that they are deep down the same thing - with efficient congruencing being the p-adic approach and decoupling the real one. 
Has this remained at a pure "moral" level - an impressionistic statement based on many similarities? Or is it an insight that has given rise to an actual dictionary between the two approaches? What has been actually carried out?
 A: Some attempts at answering this can be found in the recent Bourbaki report of L. Pierce.
A: I have a graduate student working on exactly this right now.  At present, the student has a proof of two-dimensional decoupling theorems "in the style of Wooley's argument" (replacing p-adic concepts by their Archimedean counterparts, and largely following the presentation of Pierce mentioned in the other answer), and is currently looking at the higher dimensional case.  The Wooley and Bourgain-Demeter-Guth arguments are not quite identical, but share many features in common, in particular a reliance on multi-scale iterative analysis and parabolic rescaling, and a fair amount of interpolation using Holder's inequality.  (There are however some slight differences: Bourgain-Demeter-Guth's argument explicitly relies on a multilinear Kakeya inequality which appears to be absent (or very well hidden) in Wooley's argument, while Wooley's argument seems to give slightly better quantitative bounds but is (as of our current understanding of the argument) restricted to exponents that are even integers.) I expect his thesis will contain a large part of the dictionary you are looking for, but he has another year before he finishes. 
A: Shaoming Guo, Zane Kun Li, Po-Lam Yung, and I found a bilinear proof of the decoupling inequality for the moment curve that uses the same inductive procedure as Wooley's efficient congruencing proof (Zane was the graduate student mentioned in Terry's answer from 2017).
The overall structure of the (Bourgain-Demeter-Guth) multilinear and the bilinear proofs of decoupling turned out to be quite similar, and both can be written concisely using some definitions introduced in a blog post by Tao.
However, as opposed to the multilinear argument, we do not use any Kakeya-type inequalities.
