This is the homepage of my Part III course called Restriction and Kakeya Phenomena. Here is a provisional schedule for the course. You'll be able to get notes for sections of the course, after they have been lectured, from this page. These notes might not correlate exactly with the lectures though.

Notes

1. Besicovitch sets
2. The Kakeya problem 1
3. The Kakeya problem 2
4. The circle 1
5. The circle 2
6. Discrete functional analysis
7. Riesz-Thorin interpolation
8. The discrete paraboloid 1
9. The discrete paraboloid 2
10. Montgomery's large-values conjecture and Kakeya
11. Introduction to $\Lambda(p)$ sets
12. Beckner's inequality
13. The influence of boolean functions
14. Sumsets in $\mathbb{F}_2^n$

Non-examinable handouts

Spheres

Example Sheets

Examples 1
Examples 2
Examples 3

A list of errata for the notes is now available here, and will be kept updated.

Internet Resources

 A visit to the webpage of Terry Tao is highly recommended. He has various papers, both technical and expository, on the Kakeya problem. A rather entertaining interactive guide to Besicovitch's construction is available too.

Isabella Laba also has a very useful page giving an introduction to the Kakeya Problem and connections with Harmonic analysis. Her page also summarises some of what is known in the area, and provides further links.