Connes distance and aperiodic order

Math Physics Seminar
Friday, November 14, 2014 - 14:00
1 hour (actually 50 minutes)
Skiles 005
University of Lorraine, Metz, France
We build a family of spectral triples for a discrete aperiodic tiling space, and derive the associated Connes distances. (These are non commutative geometry generalisations of Riemannian structures, and associated geodesic distances.) We show how their metric properties lead to a characterisation of high aperiodic order of the tiling. This is based on joint works with J. Kellendonk and D. Lenz.