# Mathematics Colloquia and Seminars

### A proof of $$l^2$$ decoupling for the parabola inspired from efficient congruencing
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.