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Category: stories

congrats carolyn


Rumour has it (see for example here or here)
that Carolyn Dean proved the Jacobian
conjecture
in two variables!!!
Melvin Hochster seems to have
checked the proof and is convinced it is ok. Here is what he mailed to
seminar participants

The Jacobian conjecture
in the plane has been an open problem since 1939 (Keller). The simple
statement is this: given a ring map $F$ of $C[x,y]$ (the polynomial ring
in two variables over the complex numbers $C$) to itself that fixes $C $
and sends $x, y$ to $f, $g, respectively, $F$ is an automorphism if and
only if the Jacobian determinant $f_x g_y – f_y g_x$ is a nonzero
element of $C$. The condition is easliy seen to be necessary.
Sufficiency is the challenge.

Carolyn Dean has
proved the conjecture and will give a series of talks on it beginning
Thursday, December 2, 3-4 pm, continuing on December 9 and December 16.
Because there have been at least five published incorrect proofs and
innumerable incorrect attempts, any announcement of a proof tends to be
received with skepticism. I have spent approximately one hundred hours
(beginning in mid-August) checking every detail of the argument. It is
correct.

Many congratulations Carolyn and I hope to see you once
again somewhere, sometime.

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version pi

Now
that versions 2 and 3 of my abandoned book project
noncommutative~geometry@n are being referenced (as suggested) as
“forgotten book” (see for example Michel's latest paper) it is
perhaps time to consider writing version $\\pi$. I haven't made up
my mind what to include in this version so if you had a go at these
versions (available no longer)
and have suggestions, please leave a comment. An housekeeping-note :
this blog is flooded with link-spammers recently so I did remove the
automatic posting of comments. I use the strategy proposed by Angsuman to combat
them. This sometimes means that I overlook a comment (this morning I
discovered a lost comment while cleaning up the spam-comments, sorry!)
but it is the only way to keep this blog poker-casino-sex-etc free. It
goes without saying that any relevant comment (positive or negative)
will be approved as soon as I spot it.

At the moment I
haven't the energy to start the writing phase yet, but I am slowly
preparing things

  • Emptied the big antique table upstairs
    to have plenty of place to put things.
  • Got myself a laser
    printer and put it into our home-network using AirportExpress which
    allows to turn any USB-printer into a network-printer.
  • Downloaded the Springer Verlag Book Stylefiles svmono.zip. This
    does not mean that I will submit it there (in fact, I promised at least
    one series-editor to send him a new version first) but these days I
    cannot bring myself to use AMS-stylefiles.
  • Accepted an
    invitation to give a master-course on noncommutative geometry in Granada in 2005 which, combined with
    the master-class here in Antwerp next semester may just be enough
    motivation to rewrite notes.
  • Bought all four volumes of the
    reprinted Winning Ways for your
    Mathematical Plays
    as inspiration for fancy terminology and notation
    (yes, it will be version $\\pi$ and _not_ version $e$).
  • etc.
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on fundamentalism


Politicians have a tendency to jump on bandwagons. After Theo Van
Gogh was murdered by a Dutch-Maroccan there has been a unanimous outcry
to tackle 'Muslim Fundamentalists' both in the Netherlands and
Belgium. The Belgian interior minister came on television assuring the
public that he will shut down all fundamentalist internet sites…
His teenage children should tell him some basic facts of life.
In
Belgium all politicians stumble over each other to convince us how tough
they will act against extremism (they mean of course Islamic
fundamentalism), well let us see what they will do now with the extreme
right party 'Vlaams Blok' which was convicted today (in appeal)
for racism! Nothing of course, we can all easily see fundamentalism in
other people but rarely in ourselves.
It is not a big secret that
I admire Jeanette Winterson, but rarely did I agree more with one of her
montly columns than her november column. Just one paragraph :

There is very little difference between Islamic Fundamentalism and
Christian Fundamentalism. Both groups will use holy text to justify
their murders and their misogyny. Both groups believe that they are
right and that everyone else is wrong. Both groups are anti-science,
both prefer faith over facts. Ironically, both are united against the
values of liberal Western culture.

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reading backlog

One of the things I like most about returning from a vacation is to
have an enormous pile of fresh reading : a week's worth of
newspapers, some regular mail and much more email (three quarters junk).
Also before getting into bed after the ride I like to browse through the
arXiv in search for interesting
papers.
This time, the major surprise of my initial survey came
from the newspapers. No, not Bush again, _that_ news was headline
even in France. On the other hand, I didn't hear a word about Theo Van
Gogh being shot and stabbed to death
in Amsterdam. I'll come
back to this later.
I'd rather mention the two papers that
somehow stood out during my scan of this week on the arXiv. The first is
Framed quiver moduli,
cohomology, and quantum groups
by Markus
Reineke
. By the deframing trick, a framed quiver moduli problem is
reduced to an ordinary quiver moduli problem for a dimension vector for
which one of the entries is equal to one, hence in particular, an
indivisible dimension vector. Such quiver problems are far easier to
handle than the divisible ones where everything can at best be reduced
to the classical problem of classifying tuples of $n \\times n$ matrices
up to simultaneous conjugation. Markus deals with the case when the
quiver has no oriented cycles. An important examples of a framed moduli
quiver problem _with_ oriented cycles is the study of
Brauer-Severi varieties of smooth orders. Significant progress on the
description of the fibers in this case is achieved by Raf Bocklandt,
Stijn Symens and Geert Van de Weyer and will (hopefully) be posted soon.

The second paper is Moduli schemes of rank
one Azumaya modules
by Norbert Hoffmann and Urich Stuhler which
brings back longforgotten memories of my Ph.D. thesis, 21 years
ago…

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dompnac-pourcharesse

Too exhausted, just some pictures :

  1. Dompnac 2. between Dompnac and Pourcharesse


  1. Snake near the top 4. Bifurcation
    Pourcharesse-St-Melany
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sanglier (end)


It is always rewarding to prepare a success guaranteed meal for a
large group, so we invited all people present at LeTravers at the
moment (12) for a sanglier-party on wednesday-evening.

Not
that there is so much reason to party given the outcome of the
US-elections. It is an insult to the rest of the world that a creature
who should be handed over and convicted by the International Criminal
Court for starting an illegal war can get himself re-elected. The
arrogance of an empire in decline…

It was another dry
but heavily clouded day and I spend most of it inside cooking. Perhaps
the last chance for cycling because today (thursday) it is raining
continuously. At the moment there is even thurder and lightning which
can be fairly impressive in mountanous regions. When it comes a bit
nearer all electricity will shut itself off automatically. Even with
this kind of weather the hunters go about their bizness, I just saw
one of them running with his gun on the road below (just 10 meters
away).


On a day like today there's not much to do but to sit by the
fireplace and read. I finished “Antwerp” by Nicholas
Royle. The book contains plenty of very detailed information on
Antwerp streets, building etc. which is all the more surprising as teh
author lives in Manchester. In the opening chapters he mentions two
watertowers near a railroad-bridge that I must have passed a 100 times
without noticing and only saw after reading the book… For these
details I did like the book, but I didn't get into the main plot
of the story much, so I'll give it a – in the sidebar when I get
back. At the moment I'm reading PD James' “The Murder
Room” which seems to take forever to get to the strating point
of the story, but who cares with this weather ?


But back to preparing sanglier and a few modifications to the
recipe I posted before. This time I marinated the meat for 24 hrs. in
half water/half wine, onions, garlic, carrots and herbs (oregano and
thyme). Afterwards I dried the meat and collected the juice and
vegetables in a saucepan and let it cook for 10 minutes and pulled the
mixer through it. Then I baked the wild boar in butter and garlic
until all pieces were nicely brown, poured red wine on it and the
mixed marinade. Then I let it stew for 2.5 hrs and 15 minutes before
serving I added mushrooms and a bit later some cream. The only thing I
regretted afterwards was overdoing the cream a bit, but nobody else
seemed to mind this too much.

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sanglier (bis)


Yesterday around noon the former head of the local hunting society
turned up with our reward : a huge piece of the 110kg wild boar they
shot the day before.

A reward partly for taking care of the
two lost hunting dogs the day before (one of them was his but he is
missing another two dogs at the moment so we are asked to watch out for
them) partly because the hunters have to pass 'our land'.

Each year there is a “fete des chasseurs” to thank all
local people allowingh free passage during the hunt but it is scheduled
later in the year and we are not around at that time (come to think of
it, why not this year?).

In a previous post (I'll add
links later, I do not want to waste too much time on this dial-up
connection) I mentioned that this is the only way to get wild boar meat
around here. This time there was no trade-off involved but he would
accept “un cannon” (a glass of wine, rose in his case) or
two if we insisted.

To our surprise he sais that he hadn't
eaten wild boar for over 20 years… It seems that having to slice
up the meat after the hunt isn't appetizing. Here is how they divide
the meat after the hunt : they slice the boars up into pieces (last
week-end they shot 14 op tem in Sablieres alone) and divide the parts
into more or less equal heaps (as many as the number of people taking
part in the hunt).

Then, one of them is blindfolded and when
the others point to a heap the blinfolded person has to call out a name.
This process takes a while and is accompanied with quantities of Pastis
or wine.


In previous years we got our meat nicely sliced up and packaged but
yesterday it was one huge lump of meat (probably a shoulder). So, I did
spend the better part of two hours slicing it up into pieces which is
pretty hard but indispensable work. I promised to prepare the boar by
wednesday evening (to be continued…).

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la chasse

< Monday morning 7 am : the first gunshots can be heard in the distance. As the morning progresses they come closer and one can hear the hunting dogs clearly. A bit later four or five white mini-vans race up the road and turn to get to the ridge of the mountain, each having one or more dogs inside. Fifteen minutes later, we have eyesight contact with “les chasseurs” and the gunshots are so nearby that one might consider taking cover … A typical sunday in l'Ardeche-Cevenolle (I know, it is monday but yesterday the weather was just too bad and luckily for them it's a holiday today).

The weather is really nice and as every other
addicted cyclist I want to seize the opportunity because it is highly
uncertain that there will be another dry day this week. I would like
to do my favourite round-trip : to Dompnac, then Pourcharesse and back
via St-Melany.


If you ever did this you will never forget the
Dompnac-Pourcharesse part of the trip : it is merely 4km but if you
know how to read a map you will understand what I mean. Unfortunately,
afterwards one has to descend to St-Melany crossing the hunting
forests of the community and I have no desire to end up in the
statistics as one of the over 70 deads or seriously wounded by
hunting-accidents in France every year …

So, I did
choose the second hardest (but safer) route : first to descend to the
bridge below and then climb to Sablieres (takes 15 min), descend to
the Drobie (4 mins) and then the serious climb to the highest road in
the vicinity at Peyre (takes 45 min) and back. The first time I did
the 'col de Peyre' I had to stop three times but now I know
one has to divide the thrip into three parts : the first part,
climbing to 'Le Mas' is fairly hard and by far the longest
part, after Le Mas one has a km which isn't that steep and one
needs to use this to recuperate a bit because the last part, when you
have the ridge of the mountain in sight, has still some very steep
streches. As this was my first cycling trip in the mountains in over
two months it was still pretty hard and I was glad to see the stone
pillar indicating the summit.

There was hardly any traffic :
7 cars and just 1 other cyclist. But I came across quite a few hunting
dogs that had lost their group. At first it is a bit scary to be on a
lonely road facing an unescorted dog but these hunting dogs are
usually rather nice. On the final climb back I met one who just turned
round and followed me whole the way back to LeTravers and stayed there
for the rest of the afternoon.

Later on, another lost dog
turned up and decided to stay as well. The local etiquette then
demands that you phone the owner(s) (the telephone numbers are written
on a collar they wear), which we did later on when we thought 'la
chasse' was ended for the day and the dogs were picked up around 8
pm. Unknowingly we did exactly the right thing to get our yearly piece
of fresh wild boar (to be continued)…

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connected

If this message gets posted it will mean that I finally
succeeded in connecting LeTravers to the rest of the world…
Clearly not via cable but using good old dial-in. I don't think
I'll ever see cable appearing here.

Electricity made it
appearance here only 10 years ago (and is an end-of-network setup
meaning that if two people on the mountain use a microwave, all lights
are dimmed…) and since 5 years one can reach us by telephone.

Since then I've been trying to get email working using
all sorts of (Belgian) dial-in adresses but nothing worked, the modem
didn't seem to be working. It turned out that in France you first
have to buy a special socket for the telephone outlet (costs 50FF)
which our neighbors promised to provide by the next time we came
along.

So, next time expectations were high and sure enough
I could hear the typical modem-noises until they got into an infinite
loop without ever making the connection.

Some people were
luckier but then they used a Windows-clone and even mimicking their
connection on a Mac didn't work. For some mysterious reason it
seemed that Macintosh computers (or at least their modems) were
incompatible with FranceTelecom.

Last week I did try
another option : I got a webpage with all free internet providers and
applied for a username-password with two of them (FreeFrance and
Tiscali). FreeFrance promised to send a package with the post whereas
Tiscali immediately replied with a dial-in nummer, username and
allowed me to set up my own password.

So, after driving
1000km (half of which in the pouring rain) and enjoying a glass of
rose outside in the setting sun (picture) I tried the Tiscali
connection without too much hope, but I think it works.

It
was a beautiful sunny afternoon (it seems it has been raining here
more or less continuously for the last three weeks) but at sunset the
clouds were rather threatening and sure enough the following day
(sunday) we spend the day within rain clouds.

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sanglier

Although we can hear every night (in France) wild
boar
descending the mountain in search for water and though
shooting them seems to be the only (male) social activity in Sablieres
this time of year, it is much easier to prepare a wild boar stew in
Belgium than in the Ardeche-
Cevenole
. The reason being that it is impossible to find wild boar
meat in a supermarket or butcher in the region. A few years ago we
went there in the winter and I wanted to prepare wild boar for
new-year's eve but every butcher we approached for meat replied
with a fairly angry 'ne fais pas!' as if we asked him to
perform some illegal act (which probably, unknowingly, we did…).
In contrast, supermarkets and butchers are flooded with duck
('fillet de canard', 'cuisse de canard', 'confit
de canard', you name it) but I've never spotted a living duck
in the entire region! It turned out that, in order to prevent people
from shooting boar to make a living, it is not allowed to sell wild
boar meat. The only possibility to get it is either to shoot one
yourself or to have a friend in the local hunting society (les
chasseurs, omnipresent and rather political influencial in France).
Once you managed the latter, you have to master the basics of the
exchange-trade (you always have to give one commodity to get another).
The first time we offered a bottle of Pastis (Ricard) which was
flatly rejected because to them the value of Pastis is much higher
than that of boar meat, but they would accept a bottle of wine
instead…
Anyway, here is a fairly erratic recipe for wild
boar (serves 4 to 6) as I made it on thursday : get 1kg to 1.5kg of
wild boar meat, defrost if necessary and slice it into 1-2-3cm
cubicles (don't take this too strict). Meanwhile, heat up plenty
of olive oil, slice up two fairly large onions and as much garlic as
you (and your dinner partners) can master and fry this in the oil. Add
the sliced up meat and let it fry until all pieces are nicely brown.
Add pepper and your favourite herb (which is Thyme in my case, but
Oregano or Rosemary might be other choices). Add half of bottle (or
more) of red wine and some water (change percentages if you have
younger children) and heat it up. Have a look in the refrigerator for
vegatables that would go well with the meat. This time I used carrots,
mushroom and courgettes as they were available but use your own taste
to change this. Slice up 6 big carrots and add them (in general :
slice up the harder vegetables and add them now, keep the softer
vegetables for later) and let all of this stew for 2 hrs or more on a
moderate fire (stir every 10 minutes and add wine/water when needed).
Half an hour before serving add the courgettes (or any other softer
vegetable) and 15minutes later the mushrooms. Should be accompanied
with a proper 'gratin' but as I cannot approximate the one
made by Michel, chef of camping la drobie and part-time mayor of the local
village, I went for Rosti on thursday. Enjoy!

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