Posts Tagged: Grothendieck

  • france, geometry, math, stories

    Grothendieck’s gribouillis (2)

    Posted on by

    We left the story of Grothendieck’s Lasserre notes early 2015, uncertain whether they would ever be made public. Some things have happened since. Georges Maltsiniotis gave a talk at the Gothendieck conference in Montpellier in june 2015 having as title “Grothendieck’s manuscripts in Lasserre”, raising perhaps even more questions. Philippe Douroux, a journalist at the… Read more »

  • geometry, stories

    Children have always loved colimits

    Posted on by

    If Chad Orzel is able to teach quantum theory to his dog, surely it must be possible to explain schemes, stacks, toposes and motives to hipsters? Perhaps an idea for a series of posts? It’s early days yet. So far, I’ve only added the tag sga4hipsters (pun intended) and googled around for ‘real-life’ applications of… Read more »

  • geometry, stories

    Can one explain schemes to hipsters?

    Posted on by

    Nature (the journal) asked David Mumford and John Tate (of Fields and Abel fame) to write an obituary for Alexander Grothendieck. Probably, it was their first experience ever to get a paper… rejected! What was their plan? How did they carry it out? What went wrong? And, can we learn from this? the plan Mumford… Read more »

  • geometry, stories, web

    Grothendieck’s gribouillis

    Posted on by

    A math-story well worth following in 2015. What will happen to Grothendieck’s unpublished notes, or as he preferred, his “gribouillis” (scribbles)? Here’s the little I know about this: 1. The Mormoiron scribbles During the 80ties Grothendieck lived in ‘Les Aumettes’ in Mormoiron In 1991, just before he moved to the Pyrenees he burned almost all… Read more »

  • featured, stories

    On categories, go and the book $\in$

    Posted on by

    A nice interview with Jacques Roubaud (the guy responsible for Bourbaki’s death announcement) in the courtyard of the ENS. He talks about go, categories, the composition of his book $\in$ and, of course, Grothendieck and Bourbaki. Clearly there are pop-math books like dedicated to $\pi$ or $e$, but I don’t know just one novel having… Read more »

  • books, stories

    Oulipo’s use of the Tohoku paper

    Posted on by

    Many identify the ‘Tohoku Mathematical Journal’ with just one paper published in it, affectionately called the Tohoku paper: “Sur quelques points d’algèbre homologique” by Alexander Grothendieck. In this paper, Grothendieck reshaped homological algebra for Abelian categories, extending the setting of Cartan-Eilenberg (their book and the paper both appeared in 1957). While working on the Tohoku… Read more »

  • geometry, stories

    Grothendieck’s Café

    Posted on by

    “A story says that in a Paris café around 1955 Grothendieck asked his friends “what is a scheme?”. At the time only an undefined idea of “schéma” was current in Paris, meaning more or less whatever would improve on Weil’s foundations.” (McLarty in The Rising Sea) Finding that particular café in Paris, presumably in the… Read more »

  • geometry, stories

    the birthday of Grothendieck topologies

    Posted on by

    This is the story of the day the notion of ‘neighbourhood’ changed forever (at least in the geometric sense). For ages a neighbourhood of a point was understood to be an open set of the topology containing that point. But on that day, it was demonstrated that the topology of choice of algebraic geometry, the… Read more »

  • stories

    le petit village de l’Ariège

    Posted on by

    For me this quest is over. All i did was following breadcrumbs left by others. Fellow-travelers arrived there before. What did they do next? The people from the esoteric site L’Astrée, write literary texts on Grothendieck, mixing strange details (such as the kiosque de la place Pinel, the village of Fougax-et-Barrineuf and even ‘Winnie’ or… Read more »

  • stories

    G-spots : Saint-Girons

    Posted on by

    Roy Lisker (remember him from the Mormoiron post?) has written up his Grothendieck-quest(s), available for just 23$, and with this strange blurb-text: “The author organized a committee to search for him that led to his discovery, in good health and busily at work, in September, 1996. This committee has since become the Grothendieck Biography Project…. Read more »

  • stories

    G-spots : un petit village de l’Ariège

    Posted on by

    We would love to conclude this series by finding the location of the “final” Grothendieck-spot, before his 85th birthday, this thursday. But, the road ahead will be treacherous, with imaginary villages along the way and some other traps planted by the nice people of the Grothendieck Fan Club It is well-known that some members (if… Read more »

  • stories

    G-spots : Olmet-et-Villecun

    Posted on by

    Before we start the quest for the final G-spot, hopefully in time for Grothendieck’s 85th birthday, one more post on Alexandre’s ‘hippy-days’. 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 eco-mouvement “Survivre et Vivre” (the… Read more »

  • stories

    G-spots : Massy

    Posted on by

    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 eco-movement. This iconic picture is from those days The text reads: “Schurik entre les “frères ennemis” Gaston Galan… Read more »

  • stories

    G-spots : Mormoiron

    Posted on by

    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 last-known 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 »

  • stories

    G-spots : Vendargues

    Posted on by

    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 Wikipedia-page by adding under ‘Personnalités liées à la commune’ the… Read more »

  • stories

    #cestGrothendieck

    Posted on by

    In Belgium the hashtag-craze 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 mother-in-law 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 »

  • absolute

    master seminar ncg 2011

    Posted on by

    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 »

  • stories

    the birthday of the primes=knots analogy

    Posted on by

    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 »

  • stories

    Art and the absolute point (3)

    Posted on by

    Previously, we have recalled comparisons between approaches to define a geometry over the absolute point and art-historical 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 »

  • stories

    Who dreamed up the primes=knots analogy?

    Posted on by

    One of the more surprising analogies around is that prime numbers can be viewed as knots in the 3-sphere $S^3$. 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 »

  • absolute, stories

    Art and the absolute point

    Posted on by

    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 »

  • noncommutative, web

    Grothendieck’s folly

    Posted on by

    Never a dull moment with Books Ngram Viewer. Pick your favorite topic(s) and try to explain and name valleys and peaks in the Ngram. An example. I wanted to compare the relative impact of a couple of topics I love, algebraic geometry (blue), category theory (red), representation theory (green) and noncommutative geometry (the bit of… Read more »

  • absolute, math, number theory

    Lambda-rings for formula-phobics

    Posted on by

    In 1956, Alexander Grothendieck (middle) introduced $\lambda $-rings in an algebraic-geometric context to be commutative rings A equipped with a bunch of operations $\lambda^i $ (for all numbers $i \in \mathbb{N}_+ $) satisfying a list of rather obscure identities. From the easier ones, such as $\lambda^0(x)=1, \lambda^1(x)=x, \lambda^n(x+y) = \sum_i \lambda^i(x) \lambda^{n-i}(y) $ to those… Read more »

  • absolute

    big Witt vectors for everyone (1/2)

    Posted on by

    Next time you visit your math-library, please have a look whether these books are still on the shelves : Michiel Hazewinkel‘s Formal groups and applications, William Fulton’s and Serge Lange’s Riemann-Roch algebra and Donald Knutson’s lambda-rings and the representation theory of the symmetric group. I wouldn’t be surprised if one or more of these books… Read more »

  • books, stories

    The artist and the mathematician

    Posted on by

    Over the week-end I read The artist and the mathematician (subtitle : The story of Nicolas Bourbaki, the genius mathematician who never existed) by Amir D. Aczel. Whereas the central character of the book should be Bourbaki, it focusses more on two of Bourbaki’s most colorful members, André Weil and Alexander Grothendieck, and the many… Read more »