Il Centro per la Teoria dei Topoi e le sue Applicazioni svolge ricerche altamente innovative nell’ambito della teoria dei topoi di Grothendieck, orientate allo sviluppo del ruolo unificante del concetto di topos attraverso diversi settori della matematica.
Particolare rilevanza assume in relazione a questi obiettivi la teoria dei “ponti” topos-teoretici di Olivia Caramello, coordinatrice del Centro e principal investigator del progetto pluriennale “Topos theory and its applications”.
C’est le thème du topos … qui est ce "lit", ou cette "rivière profonde", où viennent s’épouser la géométrie et l’algèbre, la topologie et l’arithmétique, la logique mathématique et la théorie des catégories, le monde du continu et celui des structures "discontinues" ou "discrètes"… Il est ce que j’ai conçu de plus vaste, pour saisir avec finesse, par un même langage riche en résonances géométriques, une "essence" commune à des situations des plus éloignées les unes des autres, provenant de telle région ou de telle autre du vaste univers des choses mathématiques.
A. Grothendieck
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