The lecture "Fourier restriction, and its applications to nonlinear dispersive equations" will be held at the University of Bonn in Summer 2026.

Time: 13th April 2026 - 20th July 2026; always on Monday, 4:15 pm - 5:45 pm. (No lecture on 25th May due to Pentecoste Holiday.) 

Location: Seminar room 1.007

Office hours: Tuesday, 10-11 am.

Here are the lecture notes, which will be updated continuously: Download 

Topics of the lectures (tbc):

1. Basic properties of the Fourier transform, motivation: Fourier restriction and nonlinear dispersive equations, non-stationary phase estimates

2. Stationary phase: Van der Corput lemma, Morse lemma, stationary phase in higher dimensions

3. Wave packet decompositions: Proof of dispersive properties for Schrödinger and wave equations.

4. Non-endpoint Strichartz estimates for SEQ: TT^* argument, Hardy-Littlewood-Sobolev inequality. Application to 1d cubic NLS.

5. Connection between Fourier restriction and dispersive equations. Strichartz for wave equations via Littlewood-Paley theory.

 More on local well-posedness: role of H^s-spaces, scaling, Persistence of regularity.

6. conservation laws for well-posed solutions, critical well-posedness for 2d SEQ, Endpoint Strichartz estimates.

7. Bilinear Strichartz estimates, proof of bilinear Fourier restriction estimates due to Tao

8. Bilinear Fourier restriction: the cone, periodic Strichartz estimates