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!

A talk on proof-theoretic aspects of Grothendieck topologies

Tomorrow (Monday 22 November 2021, at 9:40 Central European Time) I will give a talk on "Deductive systems and Grothendieck topologies" for the Dagstuhl Seminar Geometric Logic, Constructivisation, and Automated Theorem Proving.

The abstract is as follows:

I will show that the classical proof system of geometric logic over a given geometric theory is equivalent to new proof systems based on the notion of Grothendieck topology. These equivalences result from a proof-theoretic interpretation of the duality between the quotients of a given geometric theory and the subtoposes of its classifying topos. Interestingly, these alternative proof systems turn out to be computationally better-behaved than the classical one for many purposes, as I will illustrate by discussing a few selected applications.

To attend the talk, you may click here.

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.