RG Analysis and Partial Differential Equations

V5B7: Decoupling

Summer Semester 2019

Dr. Pavel Zorin-Kranich
Instructor

Lectures

  • Mo 8-10, N 0.007
  • We 8-10, N 0.007

Lecture notes

These lecture notes can be used under the CC BY-SA 4.0 license. You can ask me for access to the source code in a private repository at github. It is currently not public because it contains stuff with non-free license (which is not part of the notes) that I keep together with the notes while working on them for convenience. I also welcome suggestions for how to separate this correctly without giving up convenience of having a single repository.

I am planning to cover the following topics.

  1. Multilinear Kakeya (done)
  2. Multilinear restriction (done)
  3. Decoupling for the paraboloid (done) and the cone
  4. Local smoothing for wave equation via decoupling
  5. Limitations and would-be consequences of local smoothing
  6. Improved results for local smoothing in dimension 2+1
  7. Maximal estimate for the Schrödinger equation
  8. Brascamp-Lieb inequalities, continuity of constants
  9. Decoupling for the moment curve, Vinogradov mean value theorem

Exam

  • First period: July 15-19
  • Second period: September 23-27