My lecture dealt with the metric aspect of non-commutative geometry. The lecture consisted of two parts. The first is the proof of Theorem I.2. below (see yearly Abstract), which, thanks to the Dixmier trace, allows us to reconstruct the essential ingredients of Riemannian geometry from the Dirac operator. The second part is the determination of the fine structure of space-time based on experimental results from elementary particle physics gathered in the Glashow-Weinberg-Salam standard model. This metric structure of a dual universe is obtained by making the following assumption : the geometry of spacetime is specified by the Dirac operator that appears in the Standard Model.
Lecture