What was new for 2000:
What was new in 1999?
Dec 28, 2000
Dec 23, 2000

Added: Workshop in Partial Differential Equations in Mathematical Physics
and Applied Mathematics (Fields Institute, Toronto, April 1621), Colloque
de theorie des representations en l'honneur de Gerard Schiffman (Universite
Louis Pasteur  Strasbourg 1, Jan 2931), Ecole d'Ete Europeene de Theorie
des Groupes (CIRM, MarseilleLuminy France, July 213), Real
and Complex Harmonic analysis related to Homogeneous Manifolds (Zakopane,
Poland, Jan 11/1319), and 50 years of the Cauchy problem in Einstein's
theory of gravitation (Corsica, Jul 29Aug 10 2002). Thanks to JeanPhillipe
Anker, Piotr Chrusciel,
and Gigliola Staffilani for these conferences.
Dec 3, 2000
Dec 1, 2000
Nov 29, 2000

Added: Twelfth International Colloqium on Differential Equations (Bulgaria,
Aug 1823)

Uploaded: "Some light on
LittlewoodPaley 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 CowlingFendlerFournier.

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 :)
Nov 27, 2000
Nov 22, 2000

Uploaded: Well, it took nine months, two false starts, one promising but
horrendously complicated approach that was eventually shelved, a "retreat"
to the highdimensional case, a breakthrough, then three months of handtohand
combat, two major rewrites, a halfdozen 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.
Nov 17, 2000
Nov 13, 2000

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 wellposedness
problems, however, remain open. As for the twodimensional 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.
Nov 3, 2000
Oct 29, 2000

Linked: Local and Global wellposedness page.
This is a project, joint with Jim Colliander, Mark Keel, Gigliola Staffilani,
and Hideo Takaoka, to maintain as complete and uptodate survey as possible
of local and global wellposedness results for nonlinear dispersive and
wave equations.
Oct 23, 2000
Oct 7, 2000
Oct 4, 2000
Sep 26, 2000
Sep 6, 2000
Sep 1, 2000

Uploaded: "Does
P = NP?" slides (and one Figure).
This is a 10minute talk given at the UNSW high school math competition
prize ceremony.
Aug 15, 2000
Aug 14, 2000
Aug 9, 2000

Added: Midwest PDE 2000 Seminar
Aug 4, 2000

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 email 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.
Aug 1, 2000
July 28, 2000
July 14, 2000

Added: Milan conference on Fourier Analysis and Convexity
July 10, 2000
June 13, 2000
May 17, 2000
May 14, 2000
May 6, 2000
May 4, 2000
Apr 28, 2000
Apr 13, 2000
Apr 10, 2000
Apr 3, 2000
Mar 16, 2000
Feb 25, 2000

Updated: "Dyadic product
H^1" now includes Carleson's counterexample (i.e. product BMO != rectangular
BMO)
Feb 16, 2000
Feb 5, 2000
Feb 2, 2000
Jan 24, 2000
Jan 17, 2000
Jan 10, 2000
Jan 7, 2000
Jan 5, 2000
Jan 3, 2000