First talk out of two on the proof - the second talk can be found here.
The main new idea in the proof of decoupling has to do with combining information from different scales. This was already a central strategy in the field of restriction theory, so it came as a big surprise to me that it could be pushed dramatically further. The proof involves not just one way but several ways of combining multiple scales. We will delve into the proof, gradually proving stronger estimates as we add more refined ways to put together different scales.