Decoupling reading group

Decoupling inequalities are an important tool in Modern Harmonic Analysis with applications to PDE, harmonic analysis and analytic number theory. The reading group is based on six lectures by Jonathan Hickman (lectures 20 – 25). If you want to attend, drop me an email.

We meet on Friday at 10 in MVL14.

Past meetings

Tentative plan

1 (Lecture 20)

  • Scaling considerations for the moment curve
  • Decoupling constants
  • Stability of decoupling: the Pramanik-Seeger argument

2 Tools for proving decoupling inequalities (Lecture 21)

  • self-similarity / rescaling
  • induction on scales
  • $L^2$ orthogonality

3 More tools for proving decoupling inequalities (Lecture 22)

  • Bilinear reduction

    • Estimating the narrow part
    • Estimating the broad part
    • Combining the bounds iterating the estimate

  • Asymmetric bilinear decoupling

    • asymmetric vs symmetric

4 Decoupling for the parabola (Lecture 23)

  • Asymptotic $L^2$ orthogonality
  • Fourier slices
  • The iteration procedure

5 Decoupling for the moment curve I (Lecture 24)

  • Theorem, Non degeneracy lemma

6 Decoupling for the moment curve II (Lecture 25)