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Seminars and short courses RSS feed

Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.

CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.

For a full search interface see the Mathematics Department seminar page.

Room P3.10, Mathematics Building Instituto Superior Técnico https://tecnico.ulisboa.pt

Algebra and Topology

Joshua L. Wrigley, Université Paris Cité.

Many dualities in mathematics arise from the inherent duality of ‘syntax’ and ‘semantics’ in logic. Classical Stone duality, for example, is the syntax-semantics duality for theories of classical propositional logic, with Boolean algebras encoding the syntax of a propositional theory. The logical perspective on these ‘syntax-semantics’ dualities gives both an intuitive understanding for why mathematicians (or at least logicians) would expect these dualities to hold in the first place, as well as a framework to generalise to nearby logics.

In recent years, new ‘non-commutative’ generalisations of Stone duality have been discovered, involving inverse monoids and étale groupoids. Interestingly, this branch of duality theory was developed in the absence of a logical description. In this talk, we describe a class of logical theories whose syntax-semantics duality is given by a version of non-commutative Stone duality. Rather than originating in an exotic fragment of logic, these are theories of first-order logic which share many of the same properties as the theory of vector spaces, suggesting that non-commutative Stone duality is not so distant from classical logic as one might expect.

Current funding: FCT UIDB/04459/2020 & FCT UIDP/04459/2020.

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