connected component coalgebra

Never thought that I would ever consider Galois descent of semigroup coalgebras but in preparing for my talks for the master-class it came about naturally. Let A be a formally smooth algebra (sometimes called a quasi-free algebra, I prefer the terminology noncommutative curve) over an arbitrary base-field k. What, if anything, can be said about the connected components of the… Read more →

Brauer’s forgotten group

Non-commutative geometry seems pretty trivial compared to commutative geometry : there are just two types of manifolds, points and curves. However, nobody knows how to start classifying these non-commutative curves. I do have a conjecture that any non-commutative curve can (up to non-commutative birationality) be constructed from hereditary orders over commutative curves by universal methods but I’ll try to explain… Read more →

now I see you, now I don’t

For someone as clumsy as me, it is no real surprise to loose one in three hard disks, but what happened yesterday was a bit puzzling at first. I tried to replace the original 4 Gb hard disk of an original iMac (a tray loading iMac) following the instructions of the MacWorld : how to upgrade an iMac-page I used… Read more →

Singular via GAP on OSX

The GAP-package is very good in working with finite fields or Abelian extensions of the Rational numbers, but sooner or later we will need to use the coordinate ring or function field of an affine variety for which it is hopeless. On the other hand, there is an excellent free package to do these calculations : Singular. So, the ideal… Read more →

GAP on OS X

GAP the Groups, Algorithms, and Programming-tool (developed by two groups, one in St. Andrews, the other in Aachen) is the package if you want to work with (finite or finitely presented) groups, but it has also some routines for algebras, fields, division algebras, Lie algebras and the like. For years now it is available on MacClassic but since the last… Read more →

COLgo

COL is a map-coloring game invented by Colin Vout. Two players Left (bLack) and Right (white) take turns in coloring the map subject to the rule that no two neighboring regions may be colored the same. The last player to be able to move wins the game. For my talk on combinatorial game theory in two weeks, I choose for… Read more →

the iTunes hack

If you are interested in getting thousands of mp3-files on your computer using only 128 Kb of ROM, read on! Yesterday I made my hands dirty and with Jan’s help upgraded two 6 Gb colored iMacs (a blue and a pink one) to potential servers for our home-network having a 80 Gb resp. a 120 Gb hard disk. If you… Read more →

NOG master class update

Yesterday I made a preliminary program for the first two months of the masterclass non-commutative geometry. It is likely that the program will still undergo changes as at the moment I included only the mini-courses given by Bernhard Keller and Markus Reineke but several other people have already agreed to come and give a talk. For example, Jacques Alev (Reims),… Read more →

Bill Schelter’s Maxima

Bill Schelter was a remarkable man. First, he was a top-class mathematician. If you allow yourself to be impressed, read his proof of the Artin-Procesi theorem. Bill was also among the first to take non-commutative geometry seriously. Together with Mike Artin he investigated a notion of non-commutative integral extensions and he was the first to focuss attention to formally smooth… Read more →

bandwidth measures

One day (hopefully) lots of MP3, JPEG and perhaps even MPEG-files will be flying around our wireless home-network. But I didn’t have any idea of how much data I could cram through the Airport-connections. To estimate the available bandwith of a network there is a nice free tool around, iperf of which you can download binaries for almost any platform… Read more →

google spammers

In the GoogleMatrix I tried to understand the concept of the PageRank algorithm that Google uses to list pages according to their \’importance\’. So, if you want your webpage to come out first in a certain search, you have to increase your PageRank-value (which normally is a measure of webpages linking to your page) artificially. A method to achieve this… Read more →

an even better LaTeX system

A previous post the best LaTeX system was a commercial for Gerben Wierda’s i-Installer to get a working tetex distribution. I’ve been working happily with this TeX-system for two years now but recently run into a few (minor) problems. In the process of solving these problems I created myself a second tetex-system more or less by accident. This is what… Read more →

the google matrix

This morning there was an intriguing post on arXiv/math.RA entitled A Note on the Eigenvalues of the Google Matrix. At first I thought it was a joke but a quick Google revealed that the PageRank algorithm really is at the heart of Google technology, so I simply had to find out more about it. An extremely readable account of it… Read more →

the cpu 2 generation

Never ever tell an ICT-aware person that you want to try to set up a home-network before you understand all 65536 port-numbers and their corresponding protocols. Here is what happened to me this week. Jan Adriaenssens returned from an extended vacation in New Zealand and I told him about my problems with trying to set up WebDAV securely. He stared… Read more →

NOG master class

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… Read more →