There are other pages on the web on Kakeya and Restriction; Ben Green, Alex Iosevich, and Izabella Laba all maintain one. If you are new to this field and want to learn more, I can suggest starting with my Notices article surveying this field. If you then want to learn more about the Kakeya problem, you could try the El Escorial proceedings survey with Nets Katz, or the Edinburgh lecture notes on the Kakeya problem; if you want to learn more about the restriction problem, I can offer my Park city notes on the Restriction problem. You can also see my Math 254B home page for a more leisurelypaced introduction, but it is getting a little out of date. If you are more into the algebraic side of things, you can learn about the finite field analogues of these problems in this paper with Gerd Mockenhaupt. If you like the arithmetic combinatorial side of things, you can start with this short paper with Nets, or my Math 254A home page. If you are instead interested in the Bochner Riesz or local smoothing problems, you will have to go to my research papers, such as my second paper with Ana Vargas; I do not yet have a good survey of these problems (one should probably go look instead at the home pages of Izabella Laba or of the papers of Tom Wolff), although I mention these problems briefly in the Park city notes.
Title 
With 
Status 
Download 

Proc. Amer. Math. Soc. 124 (1996), 27972805 

The BochnerRiesz conjecture implies the restriction conjecture 

Duke Math. J. 96 (1999), 363376 

The weaktype endpoint BochnerRiesz conjecture and related topics 

Indiana U. Math. J. 47 (1998), 10971124 

A bilinear approach to the restriction and Kakeya conjectures 
Ana Vargas 
J. Amer. Math. Soc. 11 (1998), 9671000 
math.CA/9807163

On the Maximal BochnerRiesz conjecture in the plane, for p<2 

Trans. Amer. Math. Soc. 354 (2002), 19471959 

A bilinear approach to cone multipliers I. Restriction estimates 
Ana Vargas 
GAFA 10 (2000), 185215 

Ana Vargas 
GAFA10 (2000), 216258 

An improved bound on the Minkowski dimension of Besicovitch sets in R^3 
Annals of Math. 152 (2000), 383446 

Endpoint bilinear restriction theorems for the cone, and some sharp null form estimates 

Math. Z. 238 (2001), 215268 
math.CA/9909066

Bounds on arithmetic projections, and applications to the Kakeya conjecture 
Math. Res. Letters 6 (1999), 625630 

An xray transform estimate in R^n 
Revista Mat. Iber. 17 (2001), 375408 
math.CA/9909032


Some connections between the Falconer and Furstenburg conjectures 
New York J. Math. 7 (2001), 148187 

An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension 
GAFA 11 (2001), 773806 


Notices Amer. Math. Soc. 48 (2001) No 3, 294303 

Duke Math. J. 121 (2004), 3574 

New bounds for Kakeya problems 
Journal d'Analyse de Jerusalem, 87 (2002), 231263 

Recent progress on the Kakeya conjecture 
Publicacions Matematiques, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, U. Barcelona 2002, 161180 

BochnerRiesz summability for analytic functions on
the 
to appear, Comm. Anal. Geom. 

A new bound for finite field Besicovitch sets in four dimensions 

to appear, Pacific J. Math 

A sharp bilinear restriction estimate for paraboloids 

GAFA 13 (2003), 13591384 

Some recent progress on the Restriction conjecture 

submitted, Proceedings, Fourier Analysis and Convexity Workshop 

Recent progress on the Restriction conjecture 

submitted, Park
City proceedings 
Some further papers related to Kakeya and restriction
problems can be found on my PDE preprint page.
Some further papers dealing with more general aspects of harmonic analysis can be found here.
These are generally very short, toy versions of real results due to other people, and are not publicationquality. Caveat emptor. All files other than figures are in dvi format. Unlike the preprints, these articles are fluid and subject to new developments. Please let me know if you have any comments, references, etc. on any of them.
Disclaimer: Many of the notes here are based on papers written by
other people. My intention here is not to try to "beat" these
authors' work in any way, but rather to isolate the main ingredients of the
argument, which are often very beautiful, and try to present them in as simple
and brief a context as possible (often sacrificing generality, rigour, and/or
details in order to do this). Certainly I do not view these notes as
worthy of publication in a refereed journal, and are definitely inferior to the
original article in every single aspect, with the possible exception of
brevity.
Finite field analogues of the Erdos, Falconer, and Furstenburg problems 