Primes on space-filling curves

July 26, 2015

This is a variation on a theme by Ulam.  It is well-known that Ulam’s spiral is related to the high density of primes along some quadratic polynomials, as per Hardy & Littlewood’s conjecture F.

What about other curves, in particular space-filling curves like that of Peano or that of Hilbert ? Would one expect to see particular patterns ?

Well, not knowing what to expect, I’ve tried to look at Hilbert’s. Below are thus primes marked on iterations 7 and 8 of Hilbert’s curve, with also primes shown without the curve. (I’ve chosen the convention that has the first vertex at the top left corner, and I prefer not to show the quick and ugly code.)

End result : unfortunately I can’t quite spot anything too noticeable (that the primes avoid some diagonals is an easy consequence of the curve being built from units of 4 vertices, but beyond that…). Also, for some reason worpress.com wouldn’t allow my svg files, so these are uglier png versions…

primesonhilbert7 primesonhilbert7nocurve primesonhilbert8 primesonhilbert8nocurve

Short news

July 16, 2015

In no particular order:

…Pluto!

æstas

June 26, 2015

L’été dans le Luberon by decar66 on flickr

A subjective pick of recent papers

June 24, 2015

In no particular order, some interesting-looking fairly recent papers :

In other news, the Epi-Science website is progressing apparently, with the documentation dated may and june 2015 for instance.

Quick observations concerning the Séminaire Bourbaki

June 21, 2015

Since the next Séminaire Bourbaki is due to take place next saturday, it is a good opportunity to make some quick observations.

Started in 1948, its goal as an expository seminar was clear from the start: the very first exposé was by H. Cartan on the work of Koszul rather than on his own results, and many recent advances were presented at the seminar (e.g. the same year Pisot reviewed the elementary proof of the PNT by Selberg and by Erdős).

The first issues regroup several years, and in 1968 things settled on the current format : 4 sessions during the academic year, held in november, january, march, and june. The year 2014-2015 is its 67th year, and will end with the 1103th exposé. One can notice the following :

 

Most of Grothendieck’s manuscripts to be digitized

June 18, 2015

According to an article by Stéphane Foucart in Le Monde, it has been announced at the Grothendieck conference in Montpellier that :

  • about 15,000 pages of manuscripts held by the university were now in the process of being digitized (that’s the archive that was given to Jean Malgoire in the 1990’s, which in turn he donated to the university)
  • about 50,000 pages found in Grothendieck’s Lasserre home will be digited by the Bibliothèque Nationale de France (of Gallica fame), once legal hurdles are cleared, and which contain a mix of mathematical and non-mathematical texts

Let’s see : assuming 50% of mathematical content, that’s (15,000+50,000)/2=32,500 pages.  Chopping that into bunches of 200 pages, that’s about 162 books. In comparison, Euler’s Collected Works are said to fill 60 to 80 books…

Recent talks on youtube: Manolescu, Ghys, Starr

June 13, 2015

Here are some interesting videos of talks that have been put on youtube in the past month or so :

– Ciprian Manolescu in Edinburgh

– Etienne Ghys, who is the first laureate of the Clay Award for Dissemination of Mathematics (richly deserved!), on his favorite groups (a series of 8 lectures in Portuguese at IMPA)

– Jason Starr, a series of 3 lectures in Moscow

Clichés transmitted by professors of maths/physics undergraduates in France

June 8, 2015

The latest issue of Gazette des Mathématiciens, published by SMF, is out today.

Many interesting articles there, but I’d like to mention for now the one (pages 53 to 58) by Arnaud Pierrel, a PhD student in Sociology, who writes in the Parité column.

He studies students who are attending Classes Prépa Scientifiques (in short CPGE, that’s 2 years of very intensive undergraduate courses just after high school at the end of which students attempt various competitive exams to enter a variety of Schools, mainly in engineering but also in Math or Computer Science like the École Normale Supérieure in Paris, ÉNS).

One stunning statistic from Pierrel’s article, which underlines the sociological clichés that teachers are (subconsciously?) transmitting to their students,  is the following (I’ve cut some inessential details, translation below):

Dans le cadre de notre recherche sur les CPGE scientifiques, nous avons suivi une promotion d’élèves (n = 176, soit deux classes MPSI-MP et deux de PCSI-PC) au prisme de leurs […] bulletins scolaires semestriels, en relevant systématiquement les types d’appréciations qui y figuraient.
Le constat est sans appel : alors même que filles et garçons réussissent en première année aussi bien les uns que les autres (ce qu’objectivent des passages en classe étoile en 3/2 dans les mêmes proportions), les jugements professoraux diffèrent. Aux filles, le « sérieux » ; aux garçons, le « potentiel » ou les « capacités inexploitées ». Le lien entre ces jugements différenciés et la construction de la croyance en sa valeur scolaire est lui aussi patent : ceux dont le « potentiel » est souligné à trois reprises ou plus dans les bulletins semestriels tentent leur chance au concours de l’ÉNS proportionnellement trois fois plus souvent que les autres (ie. deux occurrences ou moins). De sorte que les filles, pourtant aussi souvent que les garçons dans les classes étoiles de ce lycée, sont sous-représentées parmi ceux qui ont passé le concours de l’ÉNS. Ce n’est là qu’une facette du caractère collectif de la construction de la croyance en sa valeur scolaire. Il conviendrait de souligner également le rôle des milieux sociaux d’origine […]

Rough translation :

In the framework of our study on scientific CPGE, we have followed a cohort of students (n=176, two sets of Math-Physics majors over the two years, and two sets of Physics-Chemistry majors over the two years) by the prism of the written marks and comments given by their teacher to recap each semester.

The findings are without possible contest that : even though girls and boys succeed evenly in the first year (which is objectivized by the fact that they are allowed or not in the starred second year classes [the most select classes] in the same proportions)  the judgements of the professors differ. To girls, “seriousness” ; to boys, “potential” or “inexploited abilities”.  The link between these differentiated jugdments and the construction of one’s belief in one’s academic value is also apparent : those whose “potential” is underligned three times or more attempt the ÉNS competitive exam three times more often than those whose “potential” is mentioned two times or less. To the effect that girls, even though they are in the same amount as boys in the starred classes of the CPGE under study, are under-represented among those who attempt the ÉNS competitive exam. This is only one aspect of the collective character of the construction of one’s belief in one’s academic value. The role of the social origins of the students should also be underlined […]

 

Food for thought for all those involved in teaching…

[As usual, comments are moderated and appear during daytime of the european time zone.]

Conference on Topos Theory at IHÉS in november

June 4, 2015

The controversy that Olivia Caramello very publicly had with several category theorists (see her website and the comment section of a post by Urs Schreiber) seems to have ended.

Indeed, she mentionned yesterday that she is organizing at IHÉS next november with Pierre Cartier, Alain Connes, Stéphane Dugowson and Anatole Khélif a conference on Topos Theory. (The poster has a tremendous quote from Grothendieck, which definitely has a “let’s make peace” ring to it.)

Also, there’s a 2-day tutorial by Caramello and André Joyal planned just before the conference, so that’s a friendly setting for graduate students and newcomers.

In other news, the conference held in the memory of Grothendieck at Montpellier will take place in a couple weeks, with the schedule now out.

 

Some forthcoming conferences

May 31, 2015

Still opened for registration, one finds :


The curved arch decorated with floral patterns and bearing a relief of Tyche, the goddess of victory, Temple of Hadrian, Ephesus, Turkey by Carole Raddato on flickr


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