We review the present status of gauge theories built on various quantum space–times
described by noncommutative space–times. The mathematical tools and notions underlying …

We study geodesics flows on curved quantum Riemannian geometries using a recent
formulation in terms of bimodule connections and completely positive maps. We complete …

Spectral triples from bimodule connections and Chern connections Page 1 J. Noncommut. Geom.
11 (2017), 669–701 DOI 10.4171/JNCG/11-2-7 Journal of Noncommutative Geometry © …

We perform functional-integral quantisation of the moduli of all quantum metrics defined as
square-lengths a on the edges of a Lorentzian quadrilateral graph. Noting that the partition …

We study the quantum geometry of the fuzzy sphere defined as the angular momentum
algebra [xi, xj]= 2 ı λ p ϵ ijk xk modulo setting∑ ixi 2 to a constant, using a recently …

We construct noncommutative or'quantum'Riemannian geometry on the integers as a lattice
line with its natural 2-dimensional differential structure and metric given by arbitrary non …

We apply a recent formalism of quantum geodesics to the well-known quantum Minkowski
spacetime [xi, t]= ıλ pxi with its flat quantum metric as a model of quantum gravity effects, with …

We fully solve the quantum geometry of $\Bbb Z_n $ as a polygon graph with arbitrary metric
lengths on the edges, finding a $* $-preserving quantum Levi-Civita connection which is …

A bstract Following steps analogous to classical Kaluza-Klein theory, we solve for the
quantum Riemannian geometry on C∞(M)⊗ M 2 (ℂ) in terms of classical Riemannian …

We revisit the construction of quantum Riemannian geometries on graphs starting from a
hermitian metric compatible connection, which always exists. We use this method to find …