Discrete Analysis Seminar

There are two proofs of Vinogradov's Mean Value Theorem (VMVT), the harmonic analysis decoupling proof by Bourgain, Demeter, and Guth from 2015 and the number theoretic efficient congruencing proof by Wooley from 2017. While there has been recent work illustrating the relation between these two methods, VMVT has been open since 1935. It is then natural to ask: What does old partial progress on VMVT look like in harmonic analysis language? How similar or different does it look from current decoupling proofs? We talk about an old argument that shows VMVT "asymptotically" due to Karatsuba and interpret this in decoupling language. This is ongoing work in progress with Brian Cook, Kevin Hughes, Olivier Robert, Akshat Mudgal, and Po-Lam Yung.