The proof of the l 2 Decoupling Conjecture

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Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three (2015, methodology): “But we also believe that familiarity with some of the previous papers on decouplings, especially [9], will help the reader build some gradual understanding of our method.”
Weighted restriction estimates and application to Falconer distance set problem (2018, methodology): “Theorem 3.1 and Theorem 3.2 were proved in [4] in the case m = 2 ,d = 3, via the Bourgain-Demeter 2 -decoupling theorem [2] and induction on scales.”