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NOG master class

Published January 14, 2004 by lieven


Yesterday I made reservations for lecture rooms to run the
master class on non-commutative geometry sponsored by the ESF-NOG project. We have a lecture room on
monday- and wednesday afternoon and friday the whole day which should be
enough. I will run two courses in the program : non-commutative
geometry and projects in non-commutative geometry both 30
hours. I hope that Raf Bocklandt will do most of the work on the
Geometric invariant theory course so that my contribution to it
can be minimal. Here are the first ideas of topics I want to cover in my
courses. As always, all suggestions are wellcome (just add a
comment).

non-commutative geometry : As
I am running this course jointly with Markus Reineke and as Markus will give a
mini-course on his work on non-commutative Hilbert schemes, I will explain
the theory of formally smooth algebras. I will cover most of the
paper by Joachim Cuntz and Daniel Quillen “Algebra extensions and
nonsingularity”, Journal of AMS, v.8, no. 2, 1995, 251?289. Further,
I’ll do the first section of the paper by Alexander Rosenberg and Maxim Kontsevich,
“Noncommutative smooth spaces“. Then, I will
explain some of my own work including the “One
quiver to rule them all” paper and my recent attempts to classify
all formally smooth algebras up to non-commutative birational
equivalence. When dealing with the last topic I will explain some of Aidan Schofield‘s paper
“Birational classification of moduli spaces of representations of quivers“.

projects in
non-commutative geometry : This is one of the two courses (the other
being “projects in non-commutative algebra” run by Fred Van Oystaeyen)
for which the students have to write a paper so I will take as the topic
of my talks the application of non-commutative geometry (in particular
the theory of orders in central simple algebras) to the resolution of
commutative singularities and ask the students to carry out the detailed
analysis for one of the following important classes of examples :
quantum groups at roots of unity, deformed preprojective algebras or
symplectic reflexion algebras. I will explain in much more detail three talks I gave on the subject last fall in
Luminy. But I will begin with more background material on central simple
algebras and orders.

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antwerp sprouts

Published January 13, 2004 by lieven

The
game of sprouts is a two-person game invented by John Conway and Michael Paterson in 1967 (for some
historical comments visit the encyclopedia). You just need pen and paper to
play it. Here are the rules : Two players, Left and Right, alternate
moves until no more moves are possible. In the normal game, the last
person to move is the winner. In misere play, the last person to move is
the loser. The starting position is some number of small circles called
“spots”. A move consists of drawing a new spot g and then drawing two
lines, in the loose sense, each terminating at one end at spot g and at
the other end at some other spot. (The two lines can go to different
spots or the same spot, subject to the following conditions.) The lines
drawn cannot touch or cross any line or spot along the way. Also, no
more than three lines can terminate at any spot. A spot with three lines
attached is said to be “dead”, since it cannot facilitate any further
action.

You can play sprouts online using this Java applet.
There is also an ongoing discussion about sprouts on the geometry math forum. Probably the most complete
information can be found at the world game
of sprouts association. The analysis of the game involves some nice
topology (the Euler number) and as the options for Left and Right are
the same at each position it is an impartial game and the outcome
depends on counting arguments. There is also a (joke) variation on the
game called Brussels sprouts (although some people seem to miss the point
entirely).

Some years ago I invented some variations
on sprouts making it into a partizan game (that is, at a given
position, Left and Right have different legal moves). Here are the rules
:

Cold Antwerp Sprouts : We start with n White
dots. Left is allowed to connect two White dots or a White and bLue dot
or two bLue dots and must draw an additional Red dot on the connecting
line. Right is allowed to connect two White dots, a Red and a White dot
or two Red dots and must draw an additional bLue dot on the connecting
line.

Hot Antwerp Sprouts : We start with n
White dots. Left is allowed to connect two White dots or a White and
bLue dot or two bLue dots and must draw an additional bLue dot on the
connecting line. Right is allowed to connect two White dots, a Red and a
White dot or two Red dots and must draw an additional Red dot on the
connecting line.

Although the rules look pretty
similar, the analysis of these two games in entirely different. On
february 11th I’ll give a talk on this as an example in
Combinatorial Game Theory. I will show that Cold Antwerp Sprouts
is very similar to the game of COL, whereas Hot Antwerp Sprouts resembles SNORT.

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homemade .mac

Published January 12, 2004 by lieven

The
other members of my family don’t understand what I am trying to do the
last couple of days with all those ethernet-cables, airport-stations,
computer-books and the like. ‘Improving our network’ doesn’t make
much of an impression. To them, our network is fine as it is : from
every computer one has access to the internet and to the only
house-printer and that is what they want. To them, my
computer-phase is just an occupational therapy while recovering
from the flu. Probably they are right but I am obstinate in
experimenting to prove them wrong. Not that there is much hope,
searching the web for possible fun uses of home-networks does not give
that many interesting pages. A noteworthy exception is a series of four
articles by Alan Graham for the macdevcenter
on the homemade dot-mac with OS X-project.

In
the first article Homemade Dot-Mac with OS X he explains how to
set-up a house-network (I will give a detailed account of our
home-network shortly) and firing up your Apache webserver. One nice
feature I learned from this is to connect a computer by ethernet to the
router and via an Airport card to the network (you can force this by
specifying the order of active network ports in the
SystemPreferences/Network/Show Network port configuration-pane :
first Built-in Ethernet and second Airport). This way you
get a faster connection to the internet while still connecting to the
other computers on the network. In the second part he explains how to
get yourself a free domain name even if you have (as we do) a dynamic
IP-address via a service like DynDNS. Indeed it is quite easy to set this up but
so far I failed to reach my new DNS-server from outside the network,
probably because of bad port-mapping of my old isb2lan-router.
This afternoon I just lost two hours trying to fix this (so far :
failed) as I didn’t even know how to talk to my router as I lost the
manual which is no longer online. A few Google-searches further I
learned that i just had to type http://192.168.0.1 to get at the set-up pages
(there is even a hidden page) but you shouldnt try these links
unless you are connected to one of these routers. Maybe I will need
another look at this review.

In the second
article, Homemade Dot-Mac with OS X, Part 2 he discusses in
length setting up a firewall with BrickHouse (shareware costing $25) compared to the
built-in firewall-pane in SystemPreferences/Sharing convincing me
to stay with the built-in option. Further he explains what tools one can
use to set up a homepage (stressing the iPhoto-option).Finally, and this
is the most interesting part (though a bit obscure), he hints at the
possibility of setting up your own iDisk facility either using
FTP (insecure) or WebDAV.

The third article in the
series is Homemade Dot Mac: Home Web Radio in which he
claims that one can turn the standard OS X-Apache server into an iTunes
streaming server. He uses for this purpose the QuickTime Streaming Sever which you can get for
free from the Apple site but which I think works only when you have an
X-server. It seems that all nice features require an X-server so
maybe I should consider buying one…

The (so far)
final article is Six Great Tips for Homemade Dot Mac Servers is
really interesting and I will come back to most op these possibilities
when (if) I get them to work. The for me most promising options are :
the central file server (which he synchronizes using the
shareware-product ExecutiveSync ($15 for an academic license) but
I’m experimenting also a bit with the freeware Lacie-program Silverkeeper which seems to be doing roughly the
same things. The iTunes central-hack is next on my ToDo-list as
is (at a later stage) the WebDav and the Rendezvous-idea. So it seems
I’ll prolong my occupational therapy a while…

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