• Updated: "Multilinear weighted convolution of $L^2$ functions, and applications to non-linear dispersive equations".  This is the final revision, incorporating the suggestions from the referees.  The biggest change has been the addition of a dozen or so pictures, which in retrospect should have been there from the beginning.
• Created: A very rudimentary Winter 2001 Analysis seminar page.

• Added: Workshop in Partial Differential Equations in Mathematical Physics and Applied Mathematics (Fields Institute, Toronto, April 16-21), Colloque de theorie des representations en l'honneur de Gerard Schiffman (Universite Louis Pasteur - Strasbourg 1, Jan 29-31), Ecole d'Ete Europeene de Theorie des Groupes (CIRM, Marseille-Luminy France, July 2-13), Real and Complex Harmonic analysis related to Homogeneous Manifolds (Zakopane, Poland, Jan 11/13-19), and 50 years of the Cauchy problem in Einstein's theory of gravitation (Corsica, Jul 29-Aug 10 2002).  Thanks to Jean-Phillipe Anker, Piotr Chrusciel, and Gigliola Staffilani for these conferences.

• Updated: Oscillatory Integrals and Dispersive Equations URL.  This URL will now be updated regularly, and contain information about applications, deadlines, etc.
• Created: A very rudimentary Math 254A page.  This will be a course on harmonic analysis from the perspective of the phase plane.
• Added: Nonlinear Evolution problems meeting at Oberwolfach (May 20-26) and PIMS program on Nonlinear Partial Differential Equations (Jul-Aug)
• Updated: Workshop on Fourier Analysis and Convexity link

• Updated: "Global regularity of wave maps I.  Small critical Sobolev norm in high dimension".  This is the final publication version, and should be the last revision.  My personal nemesis, the continuity argument, has been simplified to a near triviality, and one final batch of minor typoes have been found and removed.
• I'll be on semi-vacation until January 1.

• Added: Twelfth International Colloqium on Differential Equations (Bulgaria, Aug 18-23)
• Uploaded: "Some light on Littlewood-Paley theory".  This short article gives a simple counterexample to a conjecture of Rubio de Francia, and also discusses a misprint in a related paper of Cowling-Fendler-Fournier.
• Uploaded: "Global regularity of wave maps" slides.  This is for a talk I shall give at Stanford next week.  As you can see, I've invested quite some time in wave maps now - more than I have on the Kakeya problem, though still far less than what I've spent, and continue to spend, on honeycombs - and am not ready to give the subject up yet :-)

• Updated: "Global regularity of wave maps II.  Small energy in two dimensions".  Once again, there was a problem with the continuity argument, but it is fixed now.  Some more explanatory comments have been added as well, and some minor typos corrected.

• Uploaded: Well, it took nine months, two false starts, one promising but horrendously complicated approach that was eventually shelved, a "retreat" to the high-dimensional case, a breakthrough, then three months of hand-to-hand combat, two major rewrites, a half-dozen redefinitions of the Banach spaces, and countless panic attacks whenever an estimate refused to yield, but "Global regularity of wave maps II.  Small energy in two dimensions" is finally here.  That's the good news.  The bad news is that the paper is 96 pages,  of which about 65 are devoted to proving the estimates.  (And this is the short version - an earlier draft had 105 pages).  The basic problem is that in order to banish all the logarithmic divergences from the renormalized iteration argument, one needs to squeeze out several exponential gains from the standard estimates - and in the two dimensional case some of those gains need a lot of squeezing.  About the only relief is that the bilinear L^p cone estimates didn't need to be tapped to do this, although it came very close at one stage.

The paper has been through two proofreadings, but is still a little rough at the edges; I released it a little earlier than usual because of the interest I recieved in the results.  The final, submitted version should be ready by the end of the month.

• Added: Spring School on Banach Spaces (Apr 15-21) and Arkansas Spring Lecture Series (Solutions of PDE in Periodic media) (Apr 26-28).

• Updated: "Global regularity of wave maps I.  Small critical Sobolev norm in high dimension".  There were some errors in the continuity argument and elsewhere which have now been fixed.  Thanks to Sergiu Klainerman, Kenji Nakanishi, and Igor Rodnianski for pointing out these errors.  Apparently Klainerman and Rodnianski have just recently extended the regularity result to arbitrary target Lie groups.  The scattering and critical global well-posedness problems, however, remain open.  As for the two-dimensional paper, it is becoming substantially more technical than I had first anticipated (mainly because of some subtleties in the relevant linear, bilinear and trilinear estimates), but it is still progressing smoothly, and should be ready in a few weeks.

• Uploaded: Argument principle applet
• URL: I've just discovered the LINKAlert service provided by Springer.  Basically they can send you an e-mail of the table of contents and abstracts whenever one of their journals (GAFA, Math. Zeitschrift, Math Annalen, Inventiones, etc.) come out (so it's somewhat similar to the Math ArXiv (or xxx.lanl.gov) mailing list).

• Linked: Local and Global well-posedness page.  This is a project, joint with Jim Colliander, Mark Keel, Gigliola Staffilani, and Hideo Takaoka, to maintain as complete and up-to-date survey as possible of local and global well-posedness results for non-linear dispersive and wave equations.

• Updated: Midwest PDE 2000 Seminar link.
• Added: Fourth New Mexico Analysis Seminar, Riviere-Fabes symposium and Fifth International Joint Meeting of the AMS and the Sociedad Matemática Mexicana (SMM) (Special Session in Harmonic and Functional Analysis)

• Uploaded: "Recent progress on the Kakeya conjecture".  This is a survey article, joint with Nets Katz, for the El Escorial 2000 conference proceedings.
• Uploaded: "Global regularity of wave maps I.  Small critical Sobolev norm in high dimension".  I'm currently working on the two-dimensional version of this paper.

• Added: Second Pacific Rim Conference on Mathematics (Taiwan)

• Added: International Conference of Computational Harmonic Analysis (Hong Kong) and International Conference on Nonlinear Evolutionary Partial Differential Equations (China)

• Uploaded: "Honeycombs and sums of Hermitian matrices".  This is a survey article, joint with Allen Knutson on honeycombs for the Notices of the AMS.

• Uploaded: "Does P = NP?" slides (and one Figure).  This is a 10-minute talk given at the UNSW high school math competition prize ceremony.

• Uploaded: Fundamental Theorem of Calculus applet
• Uploaded: Residue Theorem applet

• Created: Diversions page.
• Uploaded: "From rotating needles to stability of waves: emerging connections between combinatorics, analysis, and PDE"
• Uploaded: "Gowers' proof of Szemeredi's theorem for progressions of length 4" expository note.
• Milestone: 550th analyst added to the list!

• Added: Midwest PDE 2000 Seminar

• I am terribly saddened to hear that Tom Wolff has recently died in an automobile accident.  It is a great loss, both personally and mathematically.
• Added: 2002 ICMS Instructional Conference on Combinatorial Aspects of Mathematical Analysis.
• Milestone: My list of harmonic analysts now has over 500 names.  Thanks to the El Escorial organizing committee for their list of participants.  Note that in many cases I only have an e-mail address, and was unable to locate a web page, partly because of language issues.  Any updated information on web pages etc. would be greatly appreciated.

• Added: SCAPDE conference / Nonlinear PDE conference in honor of Michael Crandall
• Added: 2001 Spring Central Section Meeting of the AMS (Special Session in Harmonic Analysis and Applications)
• Uploaded: "An informal outline of Wolff's local smoothing estimate" expository note.
• URL: I've recently learnt about the Mathematics Genealogy Project.  It's a fun site, and you can add your own links to the genealogy.
• News: My thesis, "Three regularity results in harmonic analysis", has recently appeared in "Topics in Analysis and Applications", World Scientific.

• Added: Spring School on Function Spaces and Interpolation
• Created: Math 2620, Semester 2 UNSW page.

• Added: Milan conference on Fourier Analysis and Convexity

• Withdrawn: "A remark on circular means of Fourier transforms of measures".  Thanks to Ana Vargas for pointing out the (rather fatal) error in the last line of the paper.
• Uploaded: "The division problem for critical regularity wave maps" expository note.

• Uploaded: "Recent progress on the Kakeya conjecture" slides.

• Uploaded: "Geometric maximal functions, oscillatory integrals, and non-linear evolution equations" slides.

• Added: 1D Schrodinger operator Summer School.

• Uploaded: "Local well-posedness for the Yang-Mills equation below the energy norm"
• Milestone: 400th harmonic analyst/PDE analyst added to the list!  (Thanks to Fabrice Planchon for the list of French micro-local analysts).
• Added: Stochastic Analysis and Harmonic Analysis, Fabes Lectures, and European Congress conferences.

• Uploaded: "An algebra for critical regularity solutions to the free wave equation" notes.
• Added: Lectures and expository notes section to the Harmonic Analysis page
• Updated: "Multilinear weighted convolution of $L^2$ functions, and applications to non-linear dispersive equations".  Some references and comments added, proofs simplified, and one false result removed. :-)

• Added: Rajchman-Zygmund-Marcinkiewicz Symposium
• Uploaded: "Multilinear weighted convolution of $L^2$ functions, and applications to non-linear dispersive equations"

• Corrected: "Endpoint bilinear restriction estimates for the cone, and some sharp null form estimates"

• Added: Spring 2000 SCAPDE
• Linked: Math 121 and Math 199 homepages.

• Uploaded: "An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension".  This is joint with Izabella Laba.

• Added: AMS 2000 Fall Western Sectional meeting (special session in Harmonic Analysis)
• Uploaded: "A Bellman function proof of the John-Nirenberg inequality" expository note
• Uploaded: A brief description of some analysis research at UCLA

• Updated:  "Dyadic product H^1" now includes Carleson's counterexample (i.e. product BMO != rectangular BMO)

• Milestone: 350th harmonic analyst added to the list!
• Uploaded: "Global well-posedness of non-linear equations below the energy norm" slides
• Added: AMS 2000 Western Sectional meeting

• Uploaded: "Abstract kernel manipulation" expository note.

• Uploaded: "Dyadic Journe's lemma" expository note.
• Added: Orthogonal polynomials conference

• Corrected: Minor errata in "Bounds on arithmetic projections, and applications to the Kakeya conjecture".
• Updated: Caltech Mathematical Physics conference link.
• Added: Memphis Partial Differential Equations conference

• Added: Workshop in oscillatory integrals and non-linear PDE (right here at UCLA/IPAM!)
• Uploaded: "Wiener's theorem" and "L^p non-invertibility of frame operators" expository notes.

• Uploaded: "Endpoint multiplier theorems of Marcinkiewicz type"
• Added: AMS 2000 and Midwest PDE conferences

• Added: Madison Nonlinear Analysis 2000 conference (apparently unrelated to the simultaneous Courant Nonlinear Analysis 2000 conference)
• Updated: Vitae
• Corrected: El Escorial link

• Uploaded: "A remark on circular means of Fourier transforms of measures"
• Created: Math 132 Section 1, Winter 2000 class page.
• Added: France PDE and NATO Special Functions conferences

• Welcome to the final year of the millennium!
• Added: "Going to extremes", "Summability of functions", and "Wave Bestiary" expository notes.
• Updated: "Dyadic pigeonhole principle" and "Hausdorff and Minkowski dimension" expository notes.
• Corrected: Bad preprints page link.  (No, not a Y2K bug).