Récoltes et Semailles

The famous autobiographical work in two volumes by Alexander Grothendieck has just been officially published by Gallimard!

This book is a must for anyone who wants to learn about the vision inspiring Grothendieck's discoveries and reflect on ethical and sociological issues in mathematics and beyond.

I have been invited by the Editor to contribute a short text presenting the book, to be included in a booklet sold together with it and also containing texts by other mathematicians. Here is it:

Lectures Grothendieckiennes

The volume of proceedings of the lecture series Lectures Grothendieckiennes given in the academic year 2017-2018 at the Ecole Normale Superieure (Paris) is now available!

This book, which celebrates Grothendieck's mathematical heritage, is prefaced by Peter Scholze and features contributions by Pierre Cartier, Olivia Caramello, Alain Connes, Laurent Lafforgue, Colin McLarty, Gilles Pisier, Jean-Jacques Szczeciniarz and Fernando Zalamea.

My contribution is available here:

The videos of the lectures are available from YouTube at this link.

An article for "Science et Vie"

In the December issue of the French magazine Science et Vie there is an article of mine on applying the philosophy of 'bridges' and invariants in the context of social science:

Any comments are welcome.

Thanks again to the Chief Editor Thomas Cavaillé-Fol for inviting me to write this contribution!

Two talks on unification and morphogenesis

Next week I shall give two (video-recorded) talks, one in Italian and another one in English, on unification and morphogenesis from a topos-theoretic perspective:

27
April2021
Topoi come 'ponti’ unificanti: una morfogenesi matematicaIn questo seminario affronterò il tema dell’unificazione in matematica, e della dualità tra unità e molteplicità, dal punto di vista della teoria dei ‘ponti’ topos-teoretici. Discuterò in particolare il senso in cui il tipo di unificazione realizzato da questa teoria rappresenta una vera e propria ‘morfogenesi matematica’, intesa come insieme di dinamiche di differenziazione a partire da un’unità.

Slides available here.
10:30 (Italian time)Synergia Seminars,
University of Urbino
28
April2021
Unification and morphogenesis: a topos-theoretic perspectiveWe shall present some philosophical principles underlying the theory of toposes as unifying `bridges' in mathematics. More specifically, after reviewing the various types of unification which occur in mathematics, we shall discuss the way in which the connections established by topos-theoretic ‘bridges’ give rise to an authentic mathematical morphogenesis.   

Slides available here.
16:00 (French time) Seminario di Logica e Filosofia della Scienza,
University of Palermo

Many thanks to the organizers of these events, Proff. Pierluigi Graziani and Gianluigi Oliveri.


On the "unifying notion" of topos

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.