Videos of the courses given by Prof. Olivia Caramello, President of our Institute, at CentraleSupélec (Université Paris-Saclay) in 2024 and 2025 are now available on our YouTube channel:
Toposes for the working mathematician
(March-April 2024)
An introduction to topos theory and its unifying role in mathematics, not assuming any prerequisites.
After presenting the necessary categorical preliminaries, it describes the basics of the theory of sheaves on topological spaces and on general sites, the concept of classifying topos and the methodology of toposes as ‘bridges’.
Relative toposes for artificial general intelligence
(June-July 2025)
The theory of relative toposes consists in methods and techniques for studying toposes in relation to each other. The course explains the basic principles of this theory and the way in which it naturally leads to the development of new, very dynamical and structural forms of modelling, both of ‘real’ entities and phenomena, and of (natural or artificial) learning processes.
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