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Toposes as ‘bridges’ for mathematics and artificial intelligence

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Speaker: Olivia Caramello
Event date: Thursday, 20 April 2023 02:30 pm - 03:30 pm
Place: Belval campus, Maison du Savoir, room 3.040


I will introduce the theory of toposes as unifying ‘bridges’, give a survey of the main results obtained so far and discuss some work in progress and future research directions on applying this theory to fundamental themes in the field of artificial intelligence, such as the development of a semantic theory of information, the modelling of deep neural networks and automated theorem proving.

About the speaker: 

Olivia Caramello is a mathematician working as Associate Professor at the University of Insubria in Como. She is also the President of the Grothendieck Institute, an Italian foundation devoted to interdisciplinary research in the mathematical sciences.

Her research has focused on investigating the role of Grothendieck toposes as unifying spaces in Mathematics and Logic.

My main contribution has been the development of the unifying theory of topos-theoretic 'bridges', consisting in methods and techniques for transferring information between distinct mathematical theories by using toposes.

These methodologies are interdisciplinary in character and, even though they find their theoretical and most natural expression in Mathematics, they can also be applied outside it, in subjects such as Physics, Computer Science, Linguistics and Philosophy.