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If you recognize where this picture was
taken, you will know that I\’m back from France. If you look closer you
will see two bikes, my own Bulls mountainbike
in front and Stijn\’s
lightweight bike behind.
If you see the relative position of the
saddles, you will know that Stijn is at least 20 cm taller. Let me add
that he is also at least 20 yrs. younger and 20 kgs. stronger and it
will be clear that I had a hard (but fun) time trying to follow him
uphill. Btw. this picture (and the next dozen or so) was taken by Jan and I\’ll try to add the next
days a couple of shots he likes more.

Since then I\’ve been
writing up a paper which I hope will be ready to put online by
september. It\’s all about using non-commutative geometry to construct
representations of arithmetic groups, a bit like the Granada Notes but with a dash of
Double Poisson
Algebras
to it.

A positive outcome of this short break is
a renewed interest in the NeverEndingBooks project, but more on this
later. For now, let me just add that Raf
decided to feed my noncommutative geometry@n (version 2)
to a printing on demand publisher. So, if you want a perfect bound
paperback version of it (for 12 Euro approx.) you\’d better email him at once (at the
moment he will order just 5 copies).

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hectic days

Hectic
days ahead! Today, there is the Ph.D. defense of Stijn Symens and the
following two days there is a meeting in Ghent where Jacques
Alev and me organize a special session on non-commutative algebra. Here
is the programme of that section

Session 1 (Friday 20 May)
— chair : Jacques Alev (Univ. Reims)

15.30-16.25 : Iain Gordon (Glasgow, United
Kingdom) : “Rational Cherednik algebras and resolutions of
symplectic
singularities”

16.25-16.35 : break

16.35-17.30 : Olivier Schiffmann (ENS Paris, France) :
“Elliptic Hall algebras and spherical Cherednik algebras”

Session 2 (Saturday 21 May) — chair : Lieven Le Bruyn
(Univ. Antwerp)

14.30-15.15 : Markus
Reineke
(Munster, Germany) : “Geometry of Quiver Moduli”

15.15-16.00 : Raf Bocklandt &
Geert Van de Weyer
(Antwerp, Belgium) : “The power of slicing in noncommutative
geometry”

Afterwards it will be time to take a short
vacation (and do some cycling in the French mountains). Here is my
reading list for next week :

The dark Eye – Ingrid
Black
: Simply because I read her previous novel The dead

Brass – Helen Walsh : I
read the first 3 or 4 pages in the shop and couldn\’t stop …

Fleshmarked Alley – Ian
Rankin
: Hey, it\’s vacation!

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nostalgia

Unlike the
cooler people out there, I haven’t received my
_pre-ordered_ copy (via AppleStore) of Tiger yet. Partly my own fault
because I couldn’t resist the temptation to bundle up with a
personalized iPod Photo!
The good news is that it buys me more time to follow the
housecleaning tips
. First, my idea was to make a CarbonCopyClooner
image of my iBook and put it on the _iMac_ upstairs which I
rarely use these days, do a clean
Tiger install
on the iBook and gradually copy over the essential
programs and files I need (and only those!). But reading the
macdev-article, I think it is better to keep my iBook running Panther
and experiment with Tiger on the redundant iMac. (Btw. unless you want
to have a copy of my Mac-installation there will be hardly a point
checking this blog the next couple of weeks as I intend to write down
all details of the Panther/Tiger switch here.)

Last week-end I
started a _Paper-rescue_ operation, that is, to find among the
multiple copies of books/papers/courses, the ones that contain all the
required material to re-TeX them and unfortunately my _archive_
is in a bad state. There is hardly a source-file left of a paper prior
to 1999 when I started putting all my papers on the arXiv.

On the other hand, I do
have saved most of my undergraduate courses. Most of them were still
using postscript-crap like _epsfig_ etc. so I had to convert all
the graphics to PDFs (merely using Preview ) and
modify the epsfig-command to _includegraphics_. So far, I
converted all my undergraduate _differential geometry_ courses
from 1998 to this year and made them available in a uniform
screen-friendly viewing format at TheLibrary/undergraduate.

There are two
ways to read the changes in these courses over the years. (1) as a shift
from _differential_ geometry to more _algebraic_ geometry
and (2) as a shift towards realism wrt.the level of our undegraduate
students. In 1998 I was still thinking
that I could teach them an easy way into Connes non-commutative standard
model but didn’t go further than the Lie group sections (maybe one day
I’ll rewrite this course as a graduate course when I ever get
reinterested in the Connes’ approach). In 1999 I had the illusion that
it might be a good idea to introduce manifolds-by-examples coming from
operads! In 2000 I gave in to the fact
that most of the students which had to follow this course were applied
mathematicians so perhaps it was a good idea to introduce them to
dynamical systems (quod non!). The 2001 course is probably the
most realistic one while still doing standard differential geometry. In
2002 I used the conifold
singularity and conifold transitions (deformations and blow-ups) as
motivation but it was clear that the students did have difficulties with
the blow-up part as they didn’t have enough experience in
_algebraic_ geometry. So the last two years I’m giving an
introduction to algebraic geometry culminating in blow-ups and some
non-commutative geometry.

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neverendingbooks.es

With the
translating help of Juan Cuadra, a shortened version of
this post did
appear in the Spanish newspaper La Voz de Almeria. Juan
graciously send me the whole newspaper, probably hoping to prepare me
for my stay in Granada!

After a
long period of sickness and frantic writing, I may just have the energy
to start blogging again on a regular basis. For starters, I re-opened
this site for (human) comments. Bots will find it hard to enter the
required 6-character code, transcribing the phonetic data. So for
example, if you see something written like ‚”upper-eye six upper-eye
upper-en upper-are three” I hope you will understand that you are
expected to enter the code I6INR3. If you encounter problems with this
plugin, please email
me
.

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writing

A long
time ago Don Passman
told me the simple “secret” for writing books : “Get up and,
before you do anything else, try to write 2 or 3 pages. If you do this
every day, by the end of the year you’ll have a pretty thick book.”

Probably the best advice ever for those who need to get a thesis or book
finished. I’ve managed to live by this rule for several months in a
row (the first half of 2000 leading to version 2 and the winter of 2001-2002
resulting in version 3) and I can recommend it to
anyone in need for some (self)dicipline. It feels just like training,
hard in the beginning but after a couple of weeks you’re addicted.
Also the pitfalls are similar. On certain days you have so much energy
that it is easy to write 10 or more pages (or in the revision process,
to revise 30 or more pages). Don’t do it! Tomorrow you will be
exhausted and you will not be able to do a single page but you will
convince yourself that it is not needed as you did more than enough the
day before. And you’ll feel and say the same thing the day after, and
the next day! and before you realize it you’ll be way behind
schedule. So, rule 1 : do 2 pages mimimun, 3 or 4 if possible but never
more than 5!

Another useful bit of advice comes from
Lewis Caroll’s ‘Through the looking glass’
in which the Red
King says

Start at the beginning, then continue until
you reach the end. Then stop.

Too many bookprojects
never get past the planning stages. It is much more fun to dream up the
perfect book than it is to write the first paragraph. Also, when the
writing on chapter X goes slow, it is tempting to begin with chapter X+1
or any other chapter that seems like more fun, and before you know
you’ll end up with a complete mess (and believe me, I know what I’m
talking about here).

Armed with these two guiding rules I began
the new year writing version pi of my book. (Oh, a marginal note : some
people seem to think that I set up ‘NeverEndingBooks’ to get my
book published. It may surely be the case that I’ll get _a_
book published there, but _the_ book I promised already a long
time ago to the EMS-publishing
house
! So, if you have an interesting bookproject for
‘NeverEndingBooks’ please contact us.) Anyway, the writing goes
slow! I’m already far behind schedule. So far I produced just over 20
pages! Part of the problem is that I want the book to be self-contained
and from past experiences with our ‘masterclass non-commutative
geometry’ I know that this means including a lot of elementary
material (it seems that sudents are eager on entering a masterclass on
non-commutative geometry without knowing the basics of either
non-commutative algebra or algebraic geometry). So. I started out with
believe it or not the definition of matrix-multiplication! But the book
has a pretty steap learning curve, by page 3 I’m already using
Grassmannians to classify left ideals in matrix-algebras! But I was
surprised how long it took me to come up with my own proofs of all this
‘trivial’ material. But the main problem is : lack of motivation.
I’m no longer convinced that one has to write technical books to aid
the younger generation. They are already far too technical!Perhaps it
would be far better to write books helping to develop creativity? But
how? And why are there so few of such books around. In fact, I know of
only one book trying to achieve this : An Invitation to General
Algebra and Universal Constructions
By George Bergman. His chapter 0
‘about the course and these notes’ comes very close to how I would
like to teach masterclass courses or how I’d love to write books if
only I’d know how. Perhaps, over the next couple of weeks, I’ll use
this weblog again to write up a micro-course on noncommutative geometry,
some people tell me they begin to miss the mathematics on this
site.

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changes

Tomorrow
I’ll give my last class of the semester (year?) so it is about time to
think about things to do (such as preparing the courses for the
“master program on noncommutative geometry”) and changes to make to
this weblog (now that it passed the 25000 mark it is time for something
different). In the sidebar I’ve added a little poll to let you guess
what changes 2005 will bring to this blog (if I find the time over
Christmas to implement it). In short, @matrix will
become the portal of a little company I’ll start up (seems
_the_ thing to do now). Here are some possible names/goals. Which
one will it be? Vote and find out after Christmas.

WebMathNess is a Web-service company helping lazy
mathematicians to set up their website and make it LaTeXRender savvy
(free restyling every 6 months).

iHomeEntertaining is a
Tech-company helping Mac-families to get most out of their valuable
computers focussing on Audio-Photo-Video streaming along their Airport-network.

SnortGipfGames is a Game-company focussing on the
mathematical side of the Gipf project
games
by distributing Snort-versions of them.

NeverendingBooks is a Publishing-company specializing
in neverending mathematical course- and book-projects offering their
hopeless authors print on demand and eprint services.

QuiverMerch is a Merchandising-company specializing in
quivers. For example, T-shirts with the tame quiver classification,
Calogero-Moser coffee mugs, Lego-boxes to construct local quivers
etc.

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Jacobian update 2

Yesterday
a comment was made to the Jacobian update post saying :

The
newest thing I heard was that the proof unfortunately was incorrect at
some point – The jacobian conjecture strikes again..?? Comment by Stefan
12/6/2004 @ 4:16 pm

Clearly I was intrigued and I
asked for more information but (so far) got no reply. Some people
approach me for the latest on this issue (I don’t know a thing about the
‘proof’ but if you do a Google on Carolyn Dean Jacobian this weblog turns up third on
the list and therefore people assume I have to know something…)
so I did try to find out what was going on. I emailed Harm Derksen who is
in Ann Arbor _and_ an expert on polynomial automorphisms, so if
someone knew something about the status of the proof, he definitely
would be the right person. Harm replied instantly, unfortunately with
sad news : it seems that the announced seminar on Carolyn’s proof is
canceled because an error has been found… For the moment at
least, the Jacobian conjecture seems to be entirely open again in two
variables (of course most people expect it to be false in three or more
variables).

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blog-stress


What would you do if 80% of your blog is owned by the
_companies_ of your Ph.D. students? First, try to talk them into
selling some of their blogshares back to the public. If this fails,
threaten never to post on your blog again until the share-price has sunk
deep enough to force them into selling. If this fails also and if you
see that the price only goes up no matter how long you remain silent, it
is time for more drastic measures. Luckily, blogshares allows the owner of a
blog to issue new shares, thereby flooding the market and stabilizing
the price. I was forced into this twice this week (the two horizontal
lines in the diagram) : on monday I issued another 5000 shares dropping
their 80% to 40% but today they acquired again 50.1% forcing me into
issuing another 1000 shares… Clearly it would be fun if more of
you out there would be buying shares of this blog (I will stick to the
1000 shares I got by claiming the blog) but I will keep on issuing new
shares whenever one player acquires more than 50%. All of this
blogshares-stuff is a bit surrealistic. In less than one week the
share-value went from 0.76 to 62.73 and the total value of all public
owned shares from 0.00 to 377383.00 and at best I wrote one reasonable
post in the same period. Oh, the stress of having to maintain an
acceptable level of postings in order to preserve the property of the
shareholders of your blog…
As if this is not enough, some
bloggers start feeling guilty because they cannot maintain their rhytm
of updates in times that they feel sick or tired. Here's what Bitch Ph.D. wrote yesterday

I think I need a break from blogging. Well,
actually I need a break from a lot of things, but blogging is optional.
Plus, I really just have nothing of substance to say right now. I hate
to be all drama-queeny, and fuck, maybe I'll change my mind if the
meds kick in tomorrow. Though actually I think they're working in
that I still feel shitty and anxious but
it's—just—manageable enough for me to function at a sort
of minimal level. Or maybe that's a placebo effect. Who the hell
knows.

Anyway , the point of this post other than to just
say I feel incredibly shitty is to be giving myself public permission to
be a shitty blogger for however long it takes until I actually want to
talk again.

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versions e and pi


Once again, it may take a while before you know why there is a
[spooks]-logo next to this message… Thanks so much for the
abundant support I received when I mentioned that I might rewrite my
'forgotten' book! There was one (1) comment

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Scottish solids

John McKay
pointed me to a few interesting links on ‘Platonic’ solids and monstrous
moonshine. If you thought that the ancient Greek discovered the five
Platonic solids, think again! They may have been the first to give a
correct proof of the classification but the regular solids were already
known in 2000BC as some
neolithic stone artifacts
discovered in Scotland show. These
Scottish solids can be visited at the Ashmolean Museum in Oxford. McKay
also points to the paper Polyhedra in physics,
chemistry and geometry
by Michael Atiyah and Paul Sutcliffe. He also
found my posts on a talk I gave on monstrous moonshine for 2nd year students earlier this year and
mentionted a few errors and updates. As these posts are on my old weblog
I’ll repost and update them here soon. For now you can already hear and
see a talk given by John McKay himself 196884=1+196883, a monstrous tale at the Fields Institute.

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