The video of my recent talk "Toposes as unifying spaces: historical aspects and prospects" at the Workshop in honor of Alexander Grothendieck’s legacy at the Universidad Nacional de Colombia is now available on YouTube:
This talk (whose slides can be downloaded here) discusses how the unifying concept of topos was introduced and conceived by Grothendieck, as well as the future prospects provided by the theory of toposes as ‘bridges’.
It is a shorter (and partially different) version of the lecture on the same subject I gave in 2018 at the ENS for the series Lectures Grothendieckiennes organized by Frédéric Jaëck (whose slides are available here):
In fact, I have recently finished writing (in French) my contribution for the Proceedings volume of that lecture series, which will be published by Spartacus: this paper can be downloaded here. An English translation is also in preparation.