SEMINAR ANNOUNCEMENT

[Tatiana Usenich]

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MATHEMATICAL PHYSICS SEMINAR
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Thursday  22 March, 4 pm, SISSA room C

Paolo Bertozzini (Chulalongkorn University - Bangkok)

Categorical Non-commutative Geometry, Gel'fand Duality and Physics

Abstract:
A well developed candidate for a theory of ``non-commutative''
(Riemannian spin)  manifolds is the notion of A.Connes' spectral
triple. Unfortunately, a suitable definition of "morphism between
non-commutative manifolds'' is still in the making and a
generalization of Gel'fand duality to the case of "spectral manifolds"
(commutative spectral triples) is not yet available.
In this talk, we will present a review of the status of our research
program on the use of categorical methods in the setting of A.Connes'
non-commutative geometry with particular emphasis on:
- definitions of morphisms/categories of spectral triples,
- categorification of Gel'fand's duality and Gel'fand duality for
spectral triples.
Finally we will also stress the relevance of "categorical
non-commutative geometry'' for the solution of structural issues in
quantum physics (hypercovariance - spectral space-time) and in the
development of our current research program in algebraic quantum
gravity.
This is an ongoing joint research with Dr.Roberto Conti and Dr.Wicharn
Lewkeeratiyutkul