
Before we start the quest for the final Gspot, hopefully in time for Grothendieck’s 85th birthday, one more post on Alexandre’s ‘hippydays’. In the second part of Allyn Jackson’s “The Life of Alexandre Grothendieck” she tells the story that AG, while touring the US to spread the gospel of the ecomouvement “Survivre et Vivre” (the… Read more »

One week from now, Alexandre Grothendieck will turn 85. Today, we’ll have a glance at his ‘wilder years’, the early 70ties, when he resigned from the IHES and became one of the leading figures in the French ecomovement. This iconic picture is from those days The text reads: “Schurik entre les “frères ennemis” Gaston Galan… Read more »

With Grothendieck’s 85th brithday coming up, march 28th, we continue our rather erratic quest to locate the spots that once meant a lot to him. Ever wondered what Grothendieck’s lastknown hideout looked like? Well, here’s the answer: (h/t gruppe eM) And, here’s the story. One of the stranger stories to be found on the web… Read more »

In a couple of days, on march 28th, Alexandre Grothendieck will turn 85. To mark the occasion we’ll run a little series, tracking down places where he used to live, hoping to entice some of these villages in the south of France to update their Wikipediapage by adding under ‘Personnalités liées à la commune’ the… Read more »

A classic among mathematical jokes is the paper in the August/September 1938 issue of the American Mathematical Monthly “A contribution to the mathematical theory of big game hunting” by one Hector Petard of Princeton who would marry, one year later, Nicolas Bourbaki’s daughter Betti. claimtoken511b561b7a5a2 There are two main sources of information on the story… Read more »

The footnote on page E. II.6 in Bourbaki’s 1970 edition of “Theorie des ensembles” reads If this is completely obvious to you, stop reading now and start getting a life. For the rest of us, it took me quite some time before i was able to parse this formula, and when i finally did, it… Read more »

According to Jean van Heijenoort, the sad state of logic in France after WW2 was largely caused by the untimely death of several key French logicians/mathematical philosophers. Prepping for my course on the history of mathematics, starting next week, i’m trying out a couple of tools, such as Timeline JS. Below, a mini timeline of… Read more »

In the spring of 2009 I did spend a fortnight dogsitting in a huge house in the countryside, belonging to my parentsinlaw, who both passed away the year before. That particular day it was raining and thundering heavily. To distract myself from the sombre and spooky atmosphere in the house I began to surf the… Read more »

Next year I’ll be teaching a master course on the “History of Mathematics” for the first time, so I’m brainstorming a bit on how to approach such a course and I would really appreciate your input. Rather than giving a chronological historic account of some period, I’d like this course to be practice oriented and… Read more »

The sporadic second Janko group $J_2$ is generated by an element of order two and one of order three and hence is a quotient of the modular group $PSL_2(\mathbb{Z}) = C_2 \ast C_3$. This Janko group has a 100dimensional permutation representation and hence there is an index 100 subgroup $G$ of the modular group such… Read more »

One of the coolest (pure math) facts in Conway’s book ONAG is the explicit construction of the algebraic closure $\overline{\mathbb{F}_2}$ of the field with two elements as the set of all ordinal numbers smaller than $(\omega^{\omega})^{\omega}$ equipped with nimber addition and multiplication. Some time ago we did run a couple of posts on this. In… Read more »

absolute, math, number theory
Quiver Grassmannians and $\mathbb{F}_1$geometry
Posted on by lievenlbReineke’s observation that any projective variety can be realized as a quiver Grassmannian is bad news: we will have to look at special representations and/or dimension vectors if we want the Grassmannian to have desirable properties. Some people still see a silver lining: it can be used to define a larger class of geometric objects… Read more »

One of the nicer tools around is bookworm arXiv which ‘is a collaboration between the Harvard Cultural Observatory, arxiv.org, and the Open Science Data Cloud. It enables you to explore lexical trends in over 700,000 eprints, spanning mathematics, physics, computer science, and statistics’ posted on the arXiv. One possible use is to explore the popularity… Read more »

The dinosaurs among you may remember that before this blog we had the ‘na&gforum’ to accompany our masterclass in noncommutative algebra & geometry. That forum ran on an early flatpanel iMac G4 which was, for lack of a better name, baptized ‘the matrix’. The original matrix did survive the unification of the three Antwerp universities… Read more »

This week i was at the conference Noncommutative Algebraic Geometry and its Applications to Physics at the Lorentz center in Leiden. It was refreshing to go to a conference where i knew only a handful of people beforehand and where everything was organized to Oberwolfach perfection. Perhaps i’ll post someday on some of the (to… Read more »

Almost three decades ago, Yuri Manin submitted the paper “New dimensions in geometry” to the 25th Arbeitstagung, Bonn 1984. It is published in its proceedings, Springer Lecture Notes in Mathematics 1111, 59101 and there’s a review of the paper available online in the Bulletin of the AMS written by Daniel Burns. In the introduction Manin… Read more »

I’ve LaTeXed $48=2 \times 24$ posts into a 114 page booklet Monsters and Moonshine for you to download. The $24$ ‘Monsters’ posts are (mostly) about finite simple (sporadic) groups : we start with the Scottish solids (hoax?), move on to the 1415 game groupoid and a new Conway $M_{13}$sliding game which uses the sporadic Mathieu… Read more »

Last fall, Matilde Marcolli gave a course at CalTech entitled Oral Presentation: The (Martial) Art of Giving Talks. The purpose of this course was to teach students “how to effectively communicate their work in seminars and conferences and how to defend it from criticism from the audience”. The lecture notes contain basic information on the… Read more »

I’ve never apologized for prolonged periods of blogsilence and have no intention to start now. But, sometimes you need to expose the things holding you back before you can turn the page and (hopefully) start afresh. Long time readers of this blog know I’ve often warned against groupthink, personality cults and the making of exaggerate… Read more »

Here are the scans of my crude prepnotes for some of the later seminartalks. These notes still contain mistakes, most of them were corrected during the talks. So, please, read these notes with both mercy are caution! Hurwitz formula imples ABC : The proof of Smirnov’s argument, but modified so that one doesn’t require an… Read more »

October 21st : Dear Diary, today’s seminar was fun, though a bit unconventional. The intention was to explain faithfully flat descent, but at the last moment i had the crazy idea to let students discover the main idea themselves (in the easiest of examples) by means of this thought experiment : “I am an alien,… Read more »

We’ve had three seminarsessions so far, and the seminarblog ‘angs+’ contains already 20 posts and counting. As blogging is not a linear activity, I will try to post here at regular intervals to report on the ground we’ve covered in the seminar, providing links to the original angs+ posts. This year’s goal is to obtain… Read more »

In Belgium the hashtagcraze of the moment is #cestjoelle. Joelle Milquet is perceived to be the dark force behind everything, from the crisis in Greece, over DSK, to your motherinlaw coming over this weekend? #cestjoelle. Sam Leith used the same meme in his book the coincidence engine. A hurricane assembling a passenger jet out of… Read more »

F_un Mathematics Hardly a ‘new’ blog, but one that is getting a new life! On its old homepage you’ll find a diagonal banner stating ‘This site has moved’ and clicking on it will guide you to its new location : cage.ugent.be/~kthas/Fun. From now on, this site will be hosted at the University of Ghent and… Read more »
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