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Category: stories

counting down

Clearly the best thing to do for me right now would be to get into
the car and drive a 1000km south to our regular place in France. The
weather should still be good enough to have lunch outside wearing only
a T-shirt, the colours of the leaves will be splendid and the grapes
'a point'. But then we all have resp. work to finish, schools
to attend and courses to teach so all of this will have to be delayed
just a little bit longer…
Some people are more fortunate.
According to her october column, Jeanette Winterson did spend most of
september in France and the daily routine she describes resembles ours
quite well. Mind you, there are differences. Whereas she goes for a
Kir I'll prefer a proper Pastis any time. She drinks the local
white wine, we go for the Rose (weather and supply permitting…)
from the Cave Cooperative 'La Cevenole' in
. She only has to cycle 4 kilometers to get into

… a remote village enjoying two bakeries, a
butcher, a greengrocer, a fabulous deli, and a bar.

For us the nearest village having all of this on offer is Joyeuse and it takes 45 minutes by
car along narrow and winding roads to get there (1hr by bicycle to,
2hrs by bicycle back). The more important facts are similar though as
Jeanette Winterson describes in her september column :

It was a good day
to slow down, and now that I am here, I will find a different rhythm,
or rather, re-find the rhythm natural to me.Of course, what’s
important to me may not be important to you, different priorities are
fine, but I think we should make intelligent choices. The fact is that
a lot of what we do isn’t a choice at all, intelligent or stupid, we
just do it passively, and wonder where the day has gone.

many days in a life?

And when it’s gone, it’s gone.

I can hear a woodpecker tapping away like me. Maybe that
woodpecker is writing its memoirs. The woodpecker can hear me tapping
too. I am right by its tree, high up, in a top turret room. This
sympathetic Morse code makes me feel part of the life of the tree. It
is easier here to belong to other life forms, other ways of life. I am
aware of all the noises, the scents, the temperature. In the city, we
spend a lot of energy shutting life out – the noise, the aggression,
the crowded feel. It is such a relief to let life in, and even as I
write those words, I wonder how bonkers we are, making a life that is
anti-life; a life where life has to be shut out.

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irrelevant list

there is no way to recover from the previous post, allow me a slow
restart by listing some of the a-typical things done this week :

  • Ate more chocolate than during the last five years

  • Drove the car more than during the rest of the year (minus

  • Didn't do any bicycle exercise

  • Only checked email in the morning (at best)

  • Didn't do any math (apart from helping

  • Didn't go in to university at

  • Drank even more coffee than usual

  • Regardless, felt exhausted every evening

  • Did far
    less web-surfing (but managed to find
    on academic blogging)

  • Cooked fast and way too
    cholestorol-rich meals

  • Ate even more chocolates

Fortunately, the semester (and teaching)
starts tomorrow!

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anyone interested

I've been here before! I mean, I did try to set up
non-commutative algebra&geometry sites before and sooner or later
they always face the same basic problems :

a :
dyspnoea : one person does not have enough fresh ideas
to keep a mathematical site updated daily so that it continues to be of
interest (at least, I'm not one of those who can).

b :
claustrophobia : the topic of non-commutative algebra
& non-commutative geometry is too wide to be covered (cornered) by
one person. More (and differing) views are needed for balance and
continued interest.

c : paranoia : if one is
not entirely naive one has to exercise some restraint trying to protect
ones research plans (or those of students) so the most interesting ideas
never even get posted!

By definition, I cannot solve problems
a) and b) on my own. All I can hope is that, now that the basic
technological problems (such as including LaTeX-code in posts) are
solved, other people are willing to contribute. For this reason I
'depersonalized' this blog : I changed the title, removed all
personal links in the sidebar and so on. I want to open up this site
(but as I said, I've tried this before without much success) to
anyone working in non-commutative algebra and/or non-commutative
geometry who is willing to contribute posts on at least a monthly basis
(or fortnightly, weekly, daily…) for the foreseeable future. At
the moment the following 'categories' of posts are available
(others can be added on request) :

  • courses : if you want
    to tell about your topic of interest in small daily or weekly pieces.
  • columns : if you want to ventilate an opinion on something
    related (even vaguely) to na&g.
  • nc-algebra : for anything
    on non-commutative algebra not in the previous categories.
  • nc-geometry : for anything on non-commutative geometry not in the
    previous categories.
  • this blog : for suggestions or
    explanations on the technology of this site.

Mind you,
I am not looking for people who seek a forum to post
their questions (such people can still add questions as comments to
related posts) but rather for people active in na&g with a personal
opinion on relevance and future of the topic.
If you are
interested in contributing, please email me and we will work
something out. I'll also post information for authors (such as, how
to include tex, how to set restrictions etc.) in a _sticky_ post

Now, problem c) : in running sites for our master class
on noncommutative geometry I've noticed that some people are more
willing to post lectures notes etc. if they know that there is some
control on who can download their material. For this reason there will
be viewing restrictions on certain posts. Such posts will get a
padlock-sign next to them in the 'recent posts' sidebar (they
will not show up in your main page, if you are not authorized to see
them). I will add another sticky on all of this soon. For now, if you
would only be willing to contribute if there was this safeguard, rest
assured, it will be there soon. All others can of course already sign-up
or wait whether any of these plans (resp. day-dreams) ever work

update (febr 2007) : still waiting
but the padlock idea is abandoned.

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explaining symmetry

PseudonomousDaughterTwo learned vector-addition at school and
important formulas such as the _Chasles-Moebius_ equation

$\forall A,B,C \in \mathbb{R}^2~:~\vec{AB}+\vec{BC} = \vec{AC} $

Last evening I helped her a bit with her homework and there was one
problem she could not do immediately (but it was a starred exercise so
you didn't have to do it, but…) :

consider a regular pentagon
with center $\vec{0} $. Prove that

$\vec{0A} + \vec{0B} +
\vec{0C} + \vec{0D} + \vec{0E} = \vec{0} $

PD2 : How would
_you_ do this? (with a tone like : I bet even you can't do
Me : Symmetry!
PD2 : Huh?
Me : Rotate the plane
1/5 turn, then $A \mapsto B $, $B \mapsto C $ and so on. So the vector
giving the sum of all five terms must be mapped to itself under this
rotation and the only vector doing this is the zero vector.
PD2 :
That cannot be the solution, you didn't take sums of vectors and all
other exercises did that.
Me : I don't care, it is an elegant
solution, you don't have to compute a thing!

But clearly
she was not convinced and I had to admit there was nothing in her
textbook preparing her for such an argument. I was about to explain that
there was even more symmetry : reflecting along a line through a vertex
giving dihedral symmetry when I saw what the _intended solution_
of the exercise was :

Me : Okay, if you _have_ to do
sums let us try this. Fix a vertex, say A. Then the sum
$\vec{0E}+\vec{0B} $ must lie on the line 0A by the parallellogram-rule
(always good to drop in a word from the textbook to gain some
trust…), similarly the sum $\vec{0C}+\vec{0D} $ must lie on the
line 0A. So you now have to do a sum of three vectors lying on the
line 0A so the result must lie on 0A
PD2 : Yes, and???
Me : But there was nothing special about $A$. I could have started with
B and do the whole argument all over again and then I would get that
the sum is a vector on the line 0B
PD2 : And the only vector
lying on both 0A and 0B is $\vec{0} $
Me : Right! But
all we did now was just redoing the symmetry argument because the line
0A is mapped to 0B
PD2 : Don't you get started on
_that symmetry_ again!

I wonder which of the two
solutions she will sell today as her own. I would love to see the face
of a teacher when a 15yr old says “Clearly that is trivial because
the zero vector is the only one left invariant under

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diy psychoanalysis

After several years of total inactivity in the DIY-sector I managed to do the following over the week-end :

  • Replace two bedroom reading lamps (at least two years overdue). We had a two-lamps-in-one IKEA thing but ThePartner’s side broke off two years ago and mine followed a year later. Since then one lamp hung in very unstable equilibrium and in the end the only way to prevent nightly accidents was to position it vertically

  • Fix the halogen spots in the kitchen (at least one year overdue). Two years ago one half of the spots went dead because the transfo overheated. I spend a week trying to find the (totally unreachable) place where it was hidden by the installers, so I wasn’t looking forward to a repeat when the second half went dead last year. Yesterday, after replacing the transfo it became clear that this time it was just a matter of faulty spots

  • Rewire the dinner room (at least three years overdue). For years an outlet was lying around on the floor. It is now replaced by a state of the art cable tray

You do not need to have a master in psychoanalysis to figure out that I am subconsciously trying to regain some control over OurHouseSystem which PseudonymousDaughterOne gave a couple of blows this week. And, running electricity errands has a much higher effect-rate than parental interference.

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driven by ambition and sloth

Here’s a part of yesterday’s post by bitch ph.d. :

But first of all I have to figure out what the hell I’m going to teach my graduate students this semester, and really more to the point, what I am not going to bother to try to cram into this class just because it’s my first graduate class and I’m feeling like teaching everything I know in one semester is a realistic and desireable possibility. Yes! Here it all is! Everything I have ever learned! Thank you, and goodnight!

Ah, the perpetual motion machine of last-minute course planning, driven by ambition and sloth!.

I’ve had similar experiences, even with undergraduate courses (in Belgium there is no fixed curriculum so the person teaching the course is responsible for its contents). If you compare the stuff I hoped to teach when I started out with the courses I’ll be giving in a few weeks, you would be more than disappointed.
The first time I taught _differential geometry 1_ (a third year course) I did include in the syllabus everything needed to culminate in an outline of Donaldson’s result on exotic structures on $\mathbb{R}^4 $ and Connes’ non-commutative GUT-model (If you want to have a good laugh, here is the set of notes). As far as I remember I got as far as classifying compact surfaces!
A similar story for the _Lie theory_ course. Until last year this was sort of an introduction to geometric invariant theory : quotient variety of conjugacy classes of matrices, moduli space of linear dynamical systems, Hilbert schemes and the classification of $GL_n $-representations (again, smile! here is the set of notes).
Compared to these (over)ambitious courses, next year’s courses are lazy sunday-afternoon walks! What made me change my mind? I learned the hard way something already known to the ancient Greeks : mathematics does not allow short-cuts, you cannot expect students to run before they can walk. Giving an over-ambitious course doesn’t offer the students a quicker road to research, but it may result in a burn-out before they get even started!

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groen moet!

One week to go before the regional and European elections and tension is rising. For me there are two crucial questions : will a racist party get more than 20% of the votes? and will the green party get over the electoral threshold of 5%? If you are not Flemish both probably require some explanation.

A month ago, the extreme right party ‘Vlaams Blok’ was convicted in court for racism and discrimination. They can still participate in the elections because they appealed and Belgian courts are extremely slow. Many people think that this conviction only applies to the party and not to people voting for it. To me, anyone still voting for a party convicted for racism says “I don’t care about society, values and the law!”

Sadly, I wouldn’t be surprised if more than 20% of the electorate will broadcast that message next week. But let us remain optimistic and look at the Vlaams Blog weblogs and their posters ridiculing the Vlaams Blok propaganda.

Then there is the Flemish green party groen!.

Usually they got between 5% and 8% of the votes with one exception in 1999 when they obtained 11%. In 1999 they went into government and among major environmental accomplishments they also voted silly laws such as introducing an electoral threshold of 5%. In last year’s elections they were the first party to be hurt by this when they dived under 4% and had not a single member of parliament left.

I have voted green at every election with one exception : early 80ties the Americans wanted to install cruise missiles in Belgium and with my twenties-naivety I thought to be able to avoid this by casting a strategic (socialist) vote. A traumatic experience because soon afterwards the missiles were flown in…

To me this partly explains the reluctance of groen! to form an alliance with the socialist party as (sadly enough) groen! is run by people of my generation (or older).

Still, in the long run there is no alternative but to form one progressive green-red party. So, I hope that, whatever happens, after the elections competent youngsters such as Tinne Van der Straeten and Els Keytsman will take control of the green party and find equally driven people in the socialist party (not entirely trivial as they seem to specialize in babes whose major accomplishment is the introduction of the sleeveless shirt ministerial look).

In case you wonder : I will vote Tinne Van der Straeten for Europe and Lieve Stallaert for the Flemish

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capita selecta

Rather than going to the NOG
III Workshop
I think it is more fun to give a talk for the Capita
-course for 2nd year students on “Monstrous Moonshine”. If
I manage to explain to them at least something, I think I am in good
shape for next year\’s Baby Geometry (first year) course. Besides,
afterwards I may decide to give some details of Borcherds\’ solution next year in my 3rd year
Geometry-course…(but this may just be a little bit
Anyway, this is what I plan to do in my
lecture : explain both sides of the McKay-observation

196 884 = 196 883 + 1

that is, I\’ll give
the action of the modular group on the upper-half plane and prove that
its fundamental domain is just C using the modular j-function (left hand
side) and sketch the importance of the Monster group and its
representation theory (right hand side). Then I\’ll mention Ogg\’s
observation that the only subgroups Gamma(0,p)+ of SL(2,Z)
for which the fundamental domain has genus zero are the prime divisors
p of teh order of the Monster and I\’ll come to moonshine
conjecture of Conway and Norton (for those students who did hear my talk
on Antwerp sprouts, yes both Conway and Simon Norton (via his
SNORT-go) did appear there too…) and if time allows it, I\’ll sketch
the main idea of the proof. Fortunately, Richard Borcherds has written
some excellent expository papers I can use (see his papers-page and I also discovered a beautiful
moonshine-page by Helena Verrill which will make my job a lot
Btw. yesterday\’s Monster was taken from her other monster story…

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25 years monstrous moonshine

Writing a survey paper is a highly underestimated task. I once
tried it out with \’Centers of generic division algebras : the
rationality problem 1965-1990\’ and it took me a lot of time and that
was on a topic with only 10 to 15 key papers to consider… The task of
writing a survey paper on a topic with any breadth must be much more
difficult. Last week, Terry Gannon posted a survey paper on the arXiv :
Monstrous Moonshine : The first twenty-five years
which gives a very readable introduction to this exciting topic. It has
a marvelous opening line :

It has been approximately
twenty-five years since John McKay remarked that

196 884 = 196 883 +

Anyone who is puzzled by this line (“So what?”)
should definitely have a go at this paper! Still not convinced? Here is
the second sentence :

That time has seen the discovery of
important structures, the establishment of another deep connection
between number theory and algebra, and a reinforcement of a new era of
cooperation between pure mathematics and mathematical

For the remaining sentences (quite a few, the paper
is 33 pages long) I happily refer you to the paper.

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