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 »

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    my first scraper

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    As far as I know (but I am fairly ignorant) the arXiv does not provide RSS feeds for a particular section, say mathRA. Still it would be a good idea for anyone having a news aggregator to follows some weblogs and news-channels having RSS syndication. So I decided to write one as my first Perl-exercise… Read more »

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    robots.txt

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    I just finished the formal lecture-part of the course Projects in non-commutative geometry (btw. I am completely exhausted after this afternoon\’s session but hopeful that some students actually may do something with my crazy ideas), springtime seems to have arrived and next week the easter-vacation starts so it may be time to have some fun… Read more »

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    Borcherds’ monster papers

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    Yesterday morning I thought that I could use some discussions I had a week before with Markus Reineke to begin to make sense of one sentence in Kontsevich’ Arbeitstagung talk Non-commutative smooth spaces : It seems plausible that Borcherds’ infinite rank algebras with Monstrous symmetry can be realized inside Hall-Ringel algebras for some small smooth… Read more »

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    chicken of the VNC

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    If I ever get our home automation system configured I’ll use my (partly broken) old iBook as my Indigo-server (or my MisterHouse-server when I brush up my Perl-knowledge). It should then run quietly put away somewhere and I don’t want to take it out every time I want to add another routine to the program…. Read more »

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    projects in noncommutative geometry

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    Tomorrow I’ll start with the course Projects in non-commutative geometry in our masterclass. The idea of this course (and its companion Projects in non-commutative algebra run by Fred Van Oystaeyen) is that students should make a small (original if possible) work, that may eventually lead to a publication. At this moment the students have seen… Read more »

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    playtime

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    I bought a couple of X10-building blocks : a tranceiver, an appliance- and a lamp-module, a computer-interface and a motion detector and started playing using the Indigo help-page. All modules worked immediately and getting them under Indigo‘s control was also no problem. Clearly it is fun to control a living room lamp and the coffee… Read more »

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    home automation, the next project??

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    I\’ve barely managed to implement the six great tips for homemade dot mac servers by Alan Graham or he is already off on a new project : Home Automation with Mac OS X. I thought that home automation only could be installed in new, highly wired, houses but I was wrong. In part 1 Alan… Read more »

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    my temporary geek code

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    I haven’t mastered by far all nuances of this fine device yet, but here it is : a first approximation to my geek code —–BEGIN GEEK CODE BLOCK—– Version: 3.1 GM d- s: a+ C+ UB+ P+ L+ E- W++ N o? K- w– O? M+ V? PS+ PE- Y+ PGP t 5? X- R-… Read more »

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    ASCII math

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    To a large extent mathematics has to do with elaborate typography. Many youngsters have been attracted over the centuries to maths because they wanted to understand the meaning of these beautiful pages filled with integrals, partial derivatives and other bizarre hieroglyphs. But now we have come to the point that this obsession for symbols is… Read more »

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    once more : synchronizing

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    Carbon Copy Cloner is a tool to make a full backup of your hard-disk on an external firewire disk or iPod. Here’s how it sells itself Have you ever wanted a simple, complete, bootable backup of your hard drive? Have you ever wanted to upgrade to a larger hard drive with minimal hassle and without… Read more »

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    nothing beats the command line

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    Over the last couple of days I’ve been experimenting a bit with different backup methods. To begin, I did try out ExecutiveSync and its successor You Syncronize but they are very, very slow. Not only did the first synchronizing of a 0.5 Gb Folder between two computers over our Airport-network took over 2.5 hrs, but… Read more »

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    noncommutative geometry 2

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    Again I spend the whole morning preparing my talks for tomorrow in the master class. Here is an outline of what I will cover : – examples of noncommutative points and curves. Grothendieck’s characterization of commutative regular algebras by the lifting property and a proof that this lifting property in the category alg of all… Read more »

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    tweedledee and tweedledum

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    Tweedledum is a first-generation iMac (233 MHz slot-loading, 192Mb RAM, No Airport) whereas Tweedledee is 2nd-generation (350 MHz front-loading, 192Mb RAM, Airport card). A couple of weeks ago I replaced their original hard-discs (4 Gb resp. 6 Gb) by fat 120 Gb discs and from this weekend they serve as our backup-facility. Tweedledee is connected… Read more »

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    noncommutative geometry

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    Today I did prepare my lectures for tomorrow for the NOG master-class on non-commutative geometry. I\’m still doubting whether it is worth TeXing my handwritten notes. Anyway, here is what I will cover tomorrow : – Examples of l-algebras (btw. l is an arbitrary field) : matrix-algebras, group-algebras lG of finite groups, polynomial algebras, free… Read more »

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    Van Eck phreaking

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    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 data-haven) and three WW2 stories : the Waterhouse-plot about cracking Enigma… Read more »

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    a noncommutative Grothendieck topology

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    We have seen that a non-commutative $l$-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 non-commutative points (that is the algebras $L_1 \\oplus … \\oplus L_k$) are the open sets of a Grothendieck-topology on $l$…. Read more »

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    Fox & Geese

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    The game of Fox and Geese is usually played on a cross-like 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… Read more »

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    SNORTgo

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    The game of SNORT was invented by Simon Norton. The rules of its SNORTgo-version are : black and white take turns in putting a stone on a go-board 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… Read more »

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    Galois and the Brauer group

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    Last time we have seen that in order to classify all non-commutative $l$-points one needs to control the finite dimensional simple algebras having as their center a finite dimensional field-extension 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… Read more »

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    iHome phase 2 ended

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    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 iMovie-files flowing from any computer to the living room (the TV-set for photo and mpeg-files and squeezebox for audio files). The last… Read more »

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    connected component coalgebra

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    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… Read more »

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    Brauer’s forgotten group

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    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… Read more »

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    now I see you, now I don’t

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    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… Read more »

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    Singular via GAP on OSX

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    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… Read more »

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    GAP on OS X

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    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… Read more »