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### A proof of \(l^2\) decoupling for the parabola inspired from efficient congruencing

**PDE and Applied Math Seminar**

Speaker: | Zane Li, UCLA |

Related Webpage: | http://www.math.ucla.edu/~zkli/ |

Location: | 2112 MSB |

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.