The Asymptotic Formula in Waring's Problem

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Vinogradov's mean value theorem via efficient congruencing, II (2011, background): “In particular, one has the bounds G̃(7) 6 112, G̃(8) 6 224 due to Boklan [5], and G̃(9) 6 365, G̃(10) 6 497, G̃(11) 6 627, G̃(12) 6 771, G̃(13) 6 934, G̃(14) 6 1112, G̃(15) 6 1307, G̃(16) 6 1517, G̃(17) 6 1747, G̃(18) 6 1992, G̃(19) 6 2255, G̃(20) 6 2534 due to Boklan and Wooley [6].”
The proof of the l 2 Decoupling Conjecture (2015, background): “This is in part motivated by connections to the Waring problem; see [4].”
Nested efficient congruencing and relatives of Vinogradov's mean value theorem (2017, background): “Current approaches to the asymptotic formula in Waring’s problem, the sharpest available estimates for the zero-free region of the Riemann zeta function, and the investigation of equidistribution modulo 1 of polynomial sequences, all depend for their success on estimates associated with Vinogradov’s”
Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three (2015, background): “See also [18] for connections to the asymptotic formula in Waring’s problem.”