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A topos-theoretic approach to non-commutative topology

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If you have a question about this talk, please contact Paul Levy.

Topology can be generalised in at least two directions: pointless topology, leading ultimately to topos theory, or noncommutative geometry. The former has the advantage that it also carries a logical structure, the latter captures quantum settings, of which the logic is not well understood generally. We discuss a construction making a generalised space in the latter sense into a generalised space in the former sense, i.e. making a noncommutative C-star algebra into a locale. This construction is interesting from a logical point of view, and leads to an adjunction for noncommutative C-star algebras that extends Gelfand duality.

This talk is part of the Theoretical computer science seminar series.

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