Contents/conteúdo

Mathematics Department Técnico Técnico

Colloquium  RSS

08/02/2001, 16:00 — 17:00 — Amphitheatre Pa1, Mathematics Building
, 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.

Colloquium_logo

The Mathematics Colloquium is a series of monthly talks organized by the Department of Mathematics of IST, aiming to be a forum for the presentation of mathematical ideas or ideas about Mathematics. The Colloquium welcomes the participation of faculty, researchers and undergraduate or graduate students, of IST or other institutions, and is seen as an opportunity of bringing together and fostering the building up of ideas in an informal atmosphere.


Organizers: Conceição Amado, Lina Oliveira e Maria João Borges.