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.

Oral exams (30 minutes) will take place on 27th and 28th July, 2026 (first examination period) and on 5th and 6th October, 2026 (second examination period). Please send an email to make an appointment.

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, Bilinear Fourier extension estimates for elliptic hypersurfaces due to Tao

8. Bilinear Fourier extension estimates for the paraboloid, II

9. Bilinear Fourier restriction for the cone, Bilinear-to-linear reduction

10. Generalizations of bilinear restriction estimates, square function estimates, Kakeya estimates

11. Bochner-Riesz estimates, local smoothing estimates for the wave equation

12. Multilinear Fourier restriction, decoupling

13. Decoupling II, Periodic Strichartz estimates, Christ-Kiselev lemma

14. Nonlinear dispersive equations on tori

Here is the teaching evaluation: Link