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Centre for Topos Theory and its Applications

The Centre for Topos Theory and its Applications (CTTA) carries out highly innovative research in the field of Grothendieck topos theory, oriented towards the development of the unifying role of the concept of topos across different areas of mathematics.

The Centre notably develops the unifying theory of topos-theoretic ‘bridges’ of Olivia Caramello, as well as the general methodologies underlying these techniques.

One of the priorities of the Centre is the training of young researchers, activity which pursues, in particular, through the awarding of doctoral studentships and post-doctoral fellowships, also in cooperation with some of the world’s top universities.

Moreover, the CTTA also organizes scientific events, schools, research visits and conferences for the general public, with the aim of fostering international scientific cooperation at all levels.

A further aim of the Centre is to experiment new forms of synergies between the sciences through a global meta-mathematical vision inspired by the topos-theoretic techniques it develops, and to promote a better, ethically responsible, integration between fundamental research and technological innovation.

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.