Mathematics Colloquia and Seminars
A proof of \(l^2\) decoupling for the parabola inspired from efficient congruencingPDE and Applied Math Seminar
|Speaker:||Zane Li, UCLA|
|Start time:||Fri, Feb 1 2019, 4:10PM|
Vinogradov's Mean Value Theorem was proven separately by Wooley's efficient congruencing method and Bourgain-Demeter-Guth's decoupling method. While similarities between the methods have been observed no precise dictionary has been written. We give a proof of \(l^2\) decoupling for the parabola inspired by efficient congruencing in two dimensions. We will mention where tools like ball inflation and \(l^2 L^2\) decoupling come into play. Making this proof quantitative also allows us to match a bound obtained by Bourgain for the discrete Fourier restriction problem in two dimensions without resorting to using the divisor bound.