Simon Henry : "Operator algebras from toposes"

Abstract. Grothendieck toposes and 

-algebras are two distinct generalizations of the concept of topological space and there is a lot of examples of objects to which one can attach both a topos and a 

-algebra in order to study there properties: dynamical systems, foliations, graphs, automaton, topological groupoids etc.

It is hence a natural question to try to understand the relation between these two sort different object.

In this talk I will explain how to attach 

-algebras and Von Neuman algebras to (reasonable) toposes, in a way that recover the -algebra attached to all the above examples. This will open the possibility to transport a lot of techniques and concept from non-commutative geometry to topos theory, and to systematize a lot of way to construct 

-algebras from geometric data.

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