Decoupling Seminar

Time: 14:00-15:00 on Wednesdays in Spring 2016

Location: Second floor seminar room of HH

Talks

1. (10 Feb) Introduction
   • Kevin (me) will introduce restriction theory and its applications along with our goals for the semester. See the notes below; these discuss the Tomas--Stein theorem and the Uncertainty Principle.
2. (17 Feb) Multi-linear theory of Bennett--Carbery--Tao
   • Sam and Pierre. In BCT paper, I would like for you to present the relationship between multi-linear Kakeya and restriction as in this paper. You do not need to prove multi-linear Kakeya. Notes of Guth on decoupling and multilinear restriction, in particular this should be useful.See Sam's notes and Pierre's notes below on Kakeya and Restriction.
3. Multi-linear Kakeya by induction on scales
   • Kirsti. Guth gave a simple proof using induction on scales to prove the main multi-linear estimate needed in 2). You can find that here. Induction on scales underlies a lot of the proofs going forward so this is an important point to communicate.
4. Towards decoupling
   • Sophie, Adelina, Min. I would like y'all to present most of these notes by Demeter. There is a bit in these notes that are important for the next part, so the people in 4 and 5 should discuss a bit how to break things down in presenting.
5. Decoupling
   • Tom and Kevin. Present Bourgain--Demeter's proof of the l^2 decoupling conjecture. See also Bourgain--Demeter's study guide.
6. Quadratic Weyl Estimates
   • Raphael and Luka. This will be our first application of decoupling to number theory. I would like you to present the main results from this paper. See also this earlier version. Tao has a good sketch of the argument in this blog post.
7. Vinogradov's mean value theorem
   • Trevor. I want you to prove VMT. Preferably first using the methods in Bourgain--Demeter--Guth that we're building on.