Life on Gaussian primes

At the moment I’m re-reading Siobhan Roberts’ biography of John Horton Conway, Genius at play – the curious mind of John Horton Conway. In fact, I’m also re-reading Alexander Masters’ biography of Simon Norton, The genius in my basement – the biography of a happy man. [full_width_image] [/full_width_image] If you’re in for a suggestion, try… Read more »

Grothendieck’s gallery No. 154

Since mid May the Montpellier part of Grothendieck’s gribouillis are online and for everyone available at the Archives Grothendieck. The story is well-known. End of June 1990, Grothendieck phoned Jean Malgoire warning him to come asap if he wanted to safeguard the better part of G’s mathematical archive, for he was making a bonfire… A… Read more »

How to dismantle scheme theory?

In several of his talks on #IUTeich, Mochizuki argues that usual scheme theory over $\mathbb{Z}$ is not suited to tackle problems such as the ABC-conjecture. The idea appears to be that ABC involves both the additive and multiplicative nature of integers, making rings into ‘2-dimensional objects’ (and clearly we use both ‘dimensions’ in the theory… Read more »

Moonshine for everyone

Today, Samuel Dehority, Xavier Gonzalez, Neekon Vafa and Roger Van Peski arXived their paper Moonshine for all finite groups. Originally, Moonshine was thought to be connected to the Monster group. McKay and Thompson observed that the first coefficients of the normalized elliptic modular invariant \[ J(\tau) = q^{-1} + 196884 q + 21493760 q^2 +… Read more »

The geometry of football

Soon, we will be teaching computational geometry courses to football commentators. If a player is going to be substituted we’ll hear sentences like: “no surprise he’s being replaced, his Voronoi cell has been shrinking since the beginning of the second half!” David Sumpter, the author of Soccermatics: Mathematical Adventures in the Beautiful Game, wrote a… Read more »

The subway singularity

The Boston subway is a complex system, spreading out from a focus at Park Street. On March 3rd, the Boylston shuttle went into service, tying together the seven principal lines, on four different levels. A day later, train 86 went missing on the Cambridge-Dorchester line. The Harvard algebraist R. Tupelo suggested the train might have… Read more »

Forgetting can’t be that hard, can it?

Geometers will tell you there are two ways to introduce affine schemes. You can use structure sheaves. That is, compute all prime ideals of your ring and turn them into a space. Then, put a sheaf of rings on this space by localisation. You’ll get your ring back taking global sections. Or, you might try… Read more »

Stirring a cup of coffee

Please allow for a couple of end-of-semester bluesy ramblings. I just finished grading the final test of the last of five courses I lectured this semester. Most of them went, I believe, rather well. As always, it was fun to teach an introductory group theory course to second year physics students. Personally, I did enjoy… Read more »

Where are Grothendieck’s writings? (2)

A couple of days ago, there was yet another article by Philippe Douroux on Grothendieck’s Lasserre writings “Inestimables mathématiques, avez-vous donc un prix?” in the French newspaper Liberation. Not that there is much news to report. I’ve posted on this before: Grothendieck’s gribouillis, Grothendieck’s gribouillis (2), and more recently Where are Grothendieck’s writings? In that… Read more »

how much to spend on (cat)books?

My favourite tags on MathOverflow are big-lists, big-picture, soft-question, reference-request and the like. Often, answers to such tagged questions contain sound reading advice, style: “road-map to important result/theory X”. Two more K to go, so let’s spend some more money. [section_title text=”Category theory”] [full_width_image] [/full_width_image] One of the problems with my master course on algebraic… Read more »

  • featured

    COLgo

    Posted on by

    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… Read more »

  • web

    the iTunes hack

    Posted on by

    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… Read more »

  • featured

    NOG master class update

    Posted on by

    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…. Read more »

  • web

    Bill Schelter’s Maxima

    Posted on by

    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… Read more »

  • web

    bandwidth measures

    Posted on by

    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… Read more »

  • web

    google spammers

    Posted on by

    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…. Read more »

  • web

    an even better LaTeX system

    Posted on by

    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… Read more »

  • web

    the google matrix

    Posted on by

    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… Read more »

  • stories

    the cpu 2 generation

    Posted on by

    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… Read more »

  • featured

    NOG master class

    Posted on by

    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… Read more »

  • featured

    antwerp sprouts

    Posted on by

    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,… Read more »

  • web

    homemade .mac

    Posted on by

    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… Read more »

  • web

    combinatorial game software

    Posted on by

    As I am going to give a talk on Combinatorial Game Theory early next month I have to update my rusty knowledge of canonical forms of two-person game positions, their temperature theory and the like. As most of the concepts in this field are recursive they are hard to work out by humans but easy… Read more »

  • web

    SSL on Mac OSX

    Posted on by

    A longer term project is to get the web-server www.matrix.ua.ac.be integrated in our home-network as an external WebDAV-server (similar to the .Mac-service offered by Apple). But as this server runs all information about the master-class on non-comutative geometry connecting to it via HTTP to use WebDAV is too great of a security risk as all… Read more »

  • stories

    one week blogging

    Posted on by

    So far I found it rather easy to post one or more messages a day as I was installing a lot of software or trying to get things working and was merely logging my progress for future reference. These notes are useful to me but probably not to the rest of the world. Another thing… Read more »

  • web

    WarChalking

    Posted on by

    What then is all this WarWalking, WarDriving, WarChalking and so on? In particular, why the aggressive War-word in them ? From what I learned, the historical origin of these terms comes from the 1983 movie “War Games” in which a kid sets up his modem to dial numbers until it finds a computer to hack… Read more »

  • web

    iMacBondiBlue

    Posted on by

    We still have an original iMac (Bondi Blue). It runs at 233 MHz, has 192Mb RAM and a hard-disk of 4Gb, so is pretty outdated. Still, when Mac OSX was introduced I had a hard time installing extra RAM in it (for this model you have to take it apart disconnecting all sorts of cables)… Read more »

  • web

    WarWalking (3)

    Posted on by

    This time we turn to Ethereal, ‘sniffing the glue that holds the Internet together’. Here is the description they give : “Ethereal is a free network protocol analyzer for Unix and Windows. It allows you to examine data from a live network or from a capture file on disk. You can interactively browse the capture… Read more »

  • web

    WarWalking (2)

    Posted on by

    MacStumbler and iStumbler are active scanners sending out probe messages to the basestations and can therefore be detected easily. Moreover, they are not able to detect closed networks. So let us move up one step in the secrecy scale and get some passive network scanners running. The first one is KisMAC which instructs the Airport… Read more »

  • web

    WarWalking (1)

    Posted on by

    What exactly is a \’WarDriver\’? WarDriver: One who locates and logs wireless access points while in motion ;[benign]. WarDriving was invented by Peter Shipley and now commonly practiced by hobbyists, hackers and security analysts worldwide. More information about this trend can be found at wardriving.com. Even if you are not into this sport, the following… Read more »

  • web

    dinner’s ready

    Posted on by

    Not all improvements to our home-network need to be high tech. Here is a very simple measure which reduces the amount of in-house shouting drastically. Often all of us are online, either to work, surf the net, MSN-chat or listening to iTunes and clearly we can easily see which other computers are on at the… Read more »

  • web

    graphite ABS can be used

    Posted on by

    I found on the net a way around the problem that a first generation graphite airport basestation is not compatible with a third generation extreme ABS. The article is called Extending AirPort’s range with multiple base stations and addresses precisely my problem (a problem that others still think is not there judging from the replies… Read more »

  • stories

    internet’s backbones

    Posted on by

    Did you ever wonder what hardware keeps the web running ? Fibre-optic cables, cross-continent cables and the like seem to be a dull subject but in the hands of Neal Stephenson. When he was doing research for his excellent book Cryptonomicon he travelled the continents following the biggest backbone cable to be laid and wrote… Read more »

  • web

    the best LaTeX system

    Posted on by

    If you are a mathematician, you’d better have a functioning TeX on your computer which I do not have at the moment as I completely erased my HD yesterday and started brand new. Some time ago this would make me slightly nervous but as I did install TeX on a number of computers recently I… Read more »

  • web

    the fink project

    Posted on by

    The Fink project ports open source Unix applications to Mac OS X which you can download either in binary format or with the full source to compile them locally on your computer. As I made a clear start with my iMac yesterday and as I am likely to need quite a few open source packages,… Read more »