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Oxford Quantum Talks Archive

Categories of spectral geometries

Paolo Bertozzini, Thammasat University
Categories, Logic and Foundations of Physics II, May 2008, Imperial College London

In A. Connes' non-commutative geometry, "spaces" are described "dually" as spectral triples. We provide an overview of some of the notions that we deem necessary for the development of a categorical framework in the context of spectral geometry, namely: (a) several notions of morphism of spectral geometries, (b) a spectral theory for commutative full C*-categories, (c) a tentative definition of strict-n-C*-categories, (d) spectral geometries over C*-categories. If time will allow, we will speculate on possible applications to foundational issues in quantum physics: categorical covariance, spectral quantum space-time and modular quantum gravity.

[video] [streaming video] [slides]