
tweedledee and tweedledum
Tweedledum is a firstgeneration iMac (233 MHz slotloading, 192Mb RAM, No Airport) whereas Tweedledee is 2ndgeneration (350 MHz frontloading, 192Mb RAM, Airport card). A couple of weeks ago I replaced their original harddiscs (4 Gb resp. 6 Gb) by fat 120 Gb discs and from this weekend they serve as our backupfacility. Tweedledee is connected […]

noncommutative geometry
Today I did prepare my lectures for tomorrow for the NOG masterclass on noncommutative geometry. I\’m still doubting whether it is worth TeXing my handwritten notes. Anyway, here is what I will cover tomorrow : – Examples of lalgebras (btw. l is an arbitrary field) : matrixalgebras, groupalgebras lG of finite groups, polynomial algebras, free…

Van Eck phreaking
This week I reread with pleasure all 918 pages of Cryptonomicon by Neal Stephenson and found out that last time I had been extremely choosy in subplots. There are 4 major plots : one contemporary (a couple of geeks trying to set up a datahaven) and three WW2 stories : the Waterhouseplot about cracking Enigma…

a noncommutative Grothendieck topology
We have seen that a noncommutative $l$point is an algebra$P=S_1 \\oplus … \\oplus S_k$with each $S_i$ a simple finite dimensional $l$algebra with center $L_i$ which is a separable extension of $l$. The centers of these noncommutative points (that is the algebras $L_1 \\oplus … \\oplus L_k$) are the open sets of a Grothendiecktopology on $l$.…

Fox & Geese
The game of Fox and Geese is usually played on a crosslike board. I learned about it from the second volume of the first edition of Winning Ways for your Mathematical Plays which is now reprinted as number 3 of the series. In the first edition, Elwyn Berlekamp, John Conway and Richard Guy claimed that…

SNORTgo
The game of SNORT was invented by Simon Norton. The rules of its SNORTgoversion are : black and white take turns in putting a stone on a goboard such that no two stones of different colour occupy neighbouring spots. In contrast to COLgo it is a hot game meaning that many of its positions are…

Galois and the Brauer group
Last time we have seen that in order to classify all noncommutative $l$points one needs to control the finite dimensional simple algebras having as their center a finite dimensional fieldextension of $l$. We have seen that the equivalence classes of simple algebras with the same center $L$ form an Abelian group, the Brauer group. The…

iHome phase 2 ended
More than a month ago I started a long term project trying to make the best of our little home network. The first couple of weeks I managed to get iTunes, iPhoto and iMoviefiles flowing from any computer to the living room (the TVset for photo and mpegfiles and squeezebox for audio files). The last…

connected component coalgebra
Never thought that I would ever consider Galois descent of semigroup coalgebras but in preparing for my talks for the masterclass it came about naturally. Let A be a formally smooth algebra (sometimes called a quasifree algebra, I prefer the terminology noncommutative curve) over an arbitrary basefield k. What, if anything, can be said about…

Brauer’s forgotten group
Noncommutative 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 noncommutative curves. I do have a conjecture that any noncommutative curve can (up to noncommutative birationality) be constructed from hereditary orders over commutative curves by universal methods…