08/02/2001, 16:00 — 17:00 — Amphitheatre Pa1, Mathematics Building
C. J. Mulvey, University of Sussex, Brighton
Quantales, \(C^\ast\)-algebras, and Computation
Quantales were introduced in order to provide a non-commutative generalisation of, on the one hand, the concepts of general topology, and, on the other, the ideas of intuitionistic logic. These considerations were motivated principally by the problems of extending Gelfand theory to non-commutative \(C^\ast\)-algebras, and of providing a constructive foundation for quantum mechanics. Given this field of interest, it is perhaps not surprising that connections began to be established at an early point with the linear logic being developed in theoretical computer science.
In this talk, we shall survey some of the progress that has been made on these diverse fronts, including the non-commutative generalisation of the Gelfand-Naimark theorem, the quantisation of the calculus of relations, and the semantics of computation. The closeness of these subjects becomes very apparent as the concepts of each become intertwined in the theory that is developed. In particular, the identification of the concept ofnon-commutative space provides a context in which these ideas interrelate critically.
