Abstract: 

In the past decade, decoupling inequalities have played a major role in breakthroughs in number theory, geometric measure theory, and PDE. In this series of talks, we will discuss the most basic case of decoupling for the parabola. Along the way, we will introduce important tools such as the wavepacket decomposition, parabolic rescaling, broad/narrow decomposition, and how Kakeya estimates play a role in decoupling. We will also introduce the heuristics that commonly guide proofs in this area of harmonic analysis by working over the p-adics (where such heuristics are rigorous). No familiarity with the p-adics or number theory will be assumed. 
 

Reference: https://arxiv.org/abs/2209.01644