Decoupling and multilinear estimates in harmonic analysis
Schedule: Meetings are Wednesdays at 4 in E17-136, starting September 10.
The minicourse will run for about six weeks.
I will have office hours on Mondays at 4 pm. You're welcome to come by and talk about the material or the problem sets. My office is E17-314.
There will be no office hours on Monday Sep. 22. (I'll be traveling.)
We will be studying the paper ``The proof of the l^2 decoupling conjecture'' by Bourgain and Demeter.
A crucial tool in the argument is the multilinear restriction estimate from the paper ``On the multilinear restriction and Kakeya estimates,'' by Bennett, Carbery, and Tao. After introducing the subject in the first lecture, we will study multilinear estimates for a couple weeks and then come back to decoupling.
The first important step in our story is the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao. Here is a short article that I wrote, giving a streamlined version of the proof: A short proof of the multilinear Kakeya inequality. The second lecture closely followed this article.
Here are some notes on the third lecture, discussing how to prove multilinear restriction from multilinear Kakeya: Notes on multilinear restriction.
Here are some notes about the last two lectures, discussing the Bourgain-Demeter decoupling theorem: Notes on decoupling , updated on Wed. Oct. 29.
Problem Sets :
I will put a few problem sets over the mini-course to chew over to help digest the papers.
Problem Set 1.
Problem Set 2.
Problem Set after lecture 4.
Problem Set for lectures 5-6 .