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”.