In a recent post I recalled Claude Levy-Strauss’ observation “In Paris, intellectuals need a new toy every 15 years”, and gave a couple of links showing that the most recent IHES-toy has been spreading to other Parisian intellectual circles in recent years.
At the time (late sixties), Levy-Strauss was criticising the ongoing Foucault-hype. It appears that, since then, the frequency of a hype cycle is getting substantially shorter.
To me, this seems like a sensible decision, moving away from (too?) general topos theory towards explicit examples having potential applications to arithmetic geometry.
On the relation between condensed sets and toposes, here’s Dustin Clausen talking about “Toposes generated by compact projectives, and the example of condensed sets”, at the “Toposes online” conference, organised by Alain Connes, Olivia Caramello and Laurent Lafforgue in 2021.
Two days ago, Clausen gave another interesting (inaugural?) talk at the IHES on “A Conjectural Reciprocity Law for Realizations of Motives”.
Olivia Caramello, who also contributed to the seminar, posts on her blog Around Toposes that the proceedings of this lectures series is now available from the SMF.
Olivia’s blogpost links also to the YouTube channel of the seminar. Several of these talks are well worth your time watching.
In 1973, Grothendieck gave three lectures series at the Department of Mathematics of SUNY at Buffalo, the first on ‘Algebraic Geometry’, the second on ‘The Theory of Algebraic Groups’ and the third one on ‘Topos Theory’.
This MathOverflow (soft) question links to this page stating:
“The copyright of all these recordings is that of the Department of Mathematics of SUNY at Buffalo to whose representatives, in particular Professors Emeritus Jack DUSKIN and Bill LAWVERE exceptional thanks are due both for the preservation and transmission of this historic archive, the only substantial archive of recordings of courses given by one of the greatest mathematicians of all time, whose work and ideas exercised arguably the most profound influence of any individual figure in shaping the mathematics of the second half od the 20th Century. The material which it is proposed to make available here, with their agreement, will form a mirror site to the principal site entitled “Grothendieck at Buffalo” (url: ).”
Sadly, the URL is still missing.
Fortunately, another answer links to the Grothendieck project Thèmes pour une Harmonie by Mateo Carmona. If you scroll down to the 1973-section, you’ll find there all of the recordings of these three Grothendieck series of talks!
To whet your appetite, here’s the first part of his talk on topos theory on April 4th, 1973:
For all subsequent recordings of his talks in the Topos Theory series on May 11th, May 18th, May 25th, May 30th, June 4th, June 6th, June 20th, June 27th, July 2nd, July 10th, July 11th and July 12th, please consult Mateo’s website (under section 1973).