
In the early days of mathblogging, one was happy to get LaTeXRender working. Some years later, the majority of mathblogs were using the, more userfriendly, wplatex plugin to turn LaTeXcode into pngimages. Today, everyone uses MathJax which works with modern CSS and web fonts instead of equation images, so equations scale with surrounding text at…

Note to students following this year’s ‘seminar noncommutative geometry’ : the seminar starts friday september 30th at 13h in room G 0.16. However, if you have another good reason to be in Ghent on thursday september 22nd, consider attending the inaugural lecture of Koen Thas at 17h in auditorium Emmy Noether, campus De Sterre, Krijgslaan… Read more »

If you’ve downloaded recently the little booklet containing the collection of my posts on the Bourbaki code, either in pdf or epubformat, cherish it. I have taken all Bourbakicode posts offline (that is, changed their visibility from ‘Public’ to ‘Private’). Here’s why. Though all speculations and the few ‘discoveries’ in these posts are entirely my… Read more »

Perhaps, the tips and tricks I did receive to turn a selection of wordpressposts into a proper ePubfile may be of use to others, so I will describe the procedure here in some detail. It makes a difference whether or not some of the posts contain TeX. This time, I’ll sketch the process for nonLaTeX… Read more »

There were some great comments by Peter before this post was taken offline. So, here they are, once again.

Last time we’ve seen that on June 3rd 1939, the very day of the Bourbaki wedding, Malraux’ movie ‘L’espoir’ had its first (private) viewing, and we mused whether Weil’s wedding card was a coded invitation to that event. But, there’s another plausible explanation why the Bourbaki wedding might have been scheduled for June 3rd :… Read more »

In preparing for next year’s ‘seminar noncommutative geometry’ I’ve converted about 30 posts to LaTeX, centering loosely around the topics students have asked me to cover : noncommutative geometry, the absolute point (aka the field with one element), and their relation to the Riemann hypothesis. The idea being to edit these posts thoroughly, add much… Read more »

Last time we discovered that the mental picture to view prime numbers as knots in $S^3$ was first dreamed up by David Mumford. Today, we’ll focus on where and when this happened. 3. When did Mazur write his unpublished preprint? According to his own website, Barry Mazur did write the paper Remarks on the Alexander… Read more »

The papers by Liliane Beaulieu on the history of the Bourbakigroup are genuine treasure troves of good stories. Though I’m mostly interested in the prewar period, some tidbits are just too good not to use somewhere, sometime, such as here on a lazy friday afternoon … In her paper Bourbaki’s art of memory she briefly… Read more »

Previously, we have recalled comparisons between approaches to define a geometry over the absolute point and arthistorical movements, first those due to Yuri I. Manin, subsequently some extra ones due to Javier Lopez Pena and Oliver Lorscheid. In these comparisons, the art trend appears to have been chosen more to illustrate a key feature of… Read more »

Penrose tilings are aperiodic tilings of the plane, made from 2 sort of tiles : kites and darts. It is well known (see for example the standard textbook tilings and patterns section 10.5) that one can describe a Penrose tiling around a given point in the plane as an infinite sequence of 0’s and 1’s,… Read more »

In an interview with readers of the Guardian, December 3rd 2010, Julian Assange made a somewhat surprising comparison between WikiLeaks and Bourbaki, sorry, The Bourbaki (sic) : “I originally tried hard for the organisation to have no face, because I wanted egos to play no part in our activities. This followed the tradition of the… Read more »

One of the more surprising analogies around is that prime numbers can be viewed as knots in the 3sphere $S^3$. The motivation behind it is that the (etale) fundamental group of $\pmb{spec}(\mathbb{Z}/(p))$ is equal to (the completion) of the fundamental group of a circle $S^1$ and that the embedding $\pmb{spec}(\mathbb{Z}/(p)) \subset \pmb{spec}(\mathbb{Z})$ embeds this circle… Read more »

Early on in this series we deciphered part of the Bourbaki wedding invitation The wedding was planned on “le 3 Cartembre, an VI” or, for nonBourbakistas, June 3rd 1939. But, why did they choose that particular day? Because the weddinginvitationjoke was concocted sometime between mid april and mid may 1939, the most probable explanation clearly… Read more »

A few years ago a student entered my office asking suggestions for his master thesis. “I’m open to any topic as long as it has nothing to do with those silly quivers!” At that time not the best of openinglines to address me and, inevitably, the most disastrous teacherstudentconversationever followed (also on my part, i’m… Read more »

Last time we did recall Manin’s comparisons between some approaches to geometry over the absolute point $\pmb{spec}(\mathbb{F}_1)$ and trends in the history of art. In the comments to that post, Javier LopezPena wrote that he and Oliver Lorscheid briefly contemplated the idea of extending Manin’s artsydictionary to all approaches they did draw on their Map… Read more »

In his paper Cyclotomy and analytic geometry over $\mathbb{F}_1$ Yuri I. Manin sketches and compares four approaches to the definition of a geometry over $\mathbb{F}_1$, the elusive field with one element. He writes : “Preparing a colloquium talk in Paris, I have succumbed to the temptation to associate them with some dominant trends in the… Read more »

The lecturers, topics and dates of the 6 minicourses in our ‘advanced master degree 2011 in noncommutative algebra and geometry’ are : February 2125 Vladimir Bavula (University of Sheffield) : Localization Theory of Rings and Modules March 711 HansJürgen Schneider (University of München) : Nichols Algebra and Root Systems April 1112 Bernhard Keller (Université Paris… Read more »

Mathblogging.org is a recent initiative and may well become the default starting place to check on the status of the mathematical blogosphere. Handy, if you want to (re)populate your RSSaggregator with interesting mathematical blogs, is their graphical presentation of (nearly) all mathblogs ordered by type : group blogs, individual researchers, teachers and educators, journalistic writers,… Read more »

Guest post by Fred Van Oystaeyen. In my book “Virtual Topology and Functorial Geometry” (Taylor and Francis, 2009) I proposed a noncommutative version of spacetime ; it is a toy model, but mathematically correct and I included a few philosophical remarks about : “What if reality is noncommutative ?”. I want to add a few… Read more »

In view or recents events & comments, some changes have been made or will be made shortly : categories : Sanitized the plethora of wordpresscategories to which posts belong. At the moment there are just 5 categories : ‘stories’ and ‘web’ (for all posts with low mathcontent) and three categories ‘level1’, ‘level2’ and ‘level3’, loosely… Read more »

Sunday january 2nd around 18hr NeBstats went crazy. Referrals clarified that the post ‘What is the knot associated to a prime?’ was picked up at Reddit/math and remained nr.1 for about a day. Now, the dust has settled, so let’s learn from the experience. A Redditmention is to a blog what doping is to a… Read more »

Last time we introduced the game of transfinite Nimbers and asked a winning move for the transfinite game with stones a at position $~(2,2) $, b at $~(4,\omega) $, c at $~(\omega+2,\omega+3) $ and d at position $~(\omega+4,\omega+1) $. Above is the unique winning move : we remove stone d and by the rectanglerule add… Read more »

Today, we will expand the game of Nimbers to higher dimensions and do some transfinite Nimber hacking. In our identification between $\mathbb{F}_{16}^* $ and 15th roots of unity, the number 8 corresponds to $\mu^6 $, whence $\sqrt{8}=\mu^3=14 $. So, if we add a stone at the diagonal position (14,14) to the Nimbersposition of last time… Read more »

Nimbers is a 2person game, winnable only if you understand the arithmetic of the finite fields $\mathbb{F}_{2^{2^n}} $ associated to Fermat 2powers. It is played on a rectangular array (say a portion of a Goboard, for practical purposes) having a finite number of stones at distinct intersections. Here’s a typical position The players alternate making… Read more »
Close