From solution counting to Fourier analysis: connections between efficient congruencing and decoupling

Wednesday, 12 July 2023

Abstract

I will discuss how one can slowly translate a version of Wooley's efficient congruencing argument into a Fourier decoupling argument. One difficulty to overcome is to understand what solution counting means in terms of Fourier analysis. For simplicity we will mostly concentrate on this dictionary between the quadratic case of Vinogradov's Mean Value Theorem and decoupling for the parabola.