æstas

L’été dans le Luberon by decar66 on flickr

A subjective pick of recent papers

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

• Special values of the Riemann Zeta function capture all real numbers, by Emre Alkan in Proc. AMS.  Shows that any real number can be approximated by a linear combination of Zeta at odd integers, with the coefficients explicitely known. Ideally, there might be something to extract that is possible to explain to undergraduates.
• Syntactic categories for Nori motives, by Luca Barbieri-Viale, Olivia Caramello and Laurent Lafforgue. (Obviously this is way over my head ; it is a collaboration that makes sense in light of the conference previously mentionned ; and this appears to be L.Lafforgue’s first collaboration, and first paper in english too.)
• Chromatic numbers of hyperbolic surfaces, by Hugo Parlier and Camille Petit to appear in Michigan Math. J.  Lots of interesting results there, including a hyperbolic surface with infinite chromatic number!
• An Interpolating Distance between Optimal Transport and Fischer-Rao, by Lenaic Chizat, Bernhard Schmitzer, Gabriel Peyré and François-Xavier Vialard, in the context of the Σ-Vision project.

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

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 :

• first exposé by someone not holding an academic position in France : Eilenberg in 1950
• first exposé in a language other than french : Tate in 1957  quickly followed by Harish-Chandra
• most cited exposé : according to Google Scholar (if I got it right) it is Grothendieck’s 1955 Produits tensoriel topologiques et espaces nucléaires
• first exposé by a woman : apparently in June 1968 took place an exposé by Claire Delaroche jointly with Kirillov (no idea whether both spoke), and for a woman alone it occured in november 1969 with Michèle Vergne
• were the work of all the Fields Medalists the topic of a seminar prior to the ICM announcements ? Nearly so, up to 1994 the only exceptions seem to have been (unless mistaken) Roth-F58 (but reviewed in the Dubreil seminar in 1956), Cohen-F66 (reviewed in november after the ICM), and Zelmanov-F94 (never reviewed!?).

 

Most of Grothendieck’s manuscripts to be digitized

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

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

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

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.