Efficient congruencing and Fourier decoupling

The Vinogradov mean value theorem can be established in two seemingly different ways, namely the Fourier decoupling argument of Bourgain, Demeter and Guth, and the efficient congruencing argument of Wooley. We will explore the relationship between these two approaches, and describe how Wooley's argument can be adapted to give an alternative proof of Fourier decoupling. Joint work with Shaoming Guo, Zane Kun Li and Pavel Zorin-Kranich.