This article reviews the present status of the spin-foam approach to the quantization of
gravity. Special attention is payed to the pedagogical presentation of the recently-introduced …

The problem of describing the quantum behavior of gravity, and thus understanding
quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this …

Colored tensor models have recently burst onto the scene as a promising conceptual and
computational tool in the investigation of problems of random geometry in dimension three …

We extend the definition of the “flipped” loop-quantum-gravity vertex to the case of a finite
Immirzi parameter γ. We cover both the Euclidean and Lorentzian cases. We show that the …

Simplicial complexes are generalized network structures able to encode interactions
occurring between more than two nodes. Simplicial complexes describe a large variety of …

In this topical review, we review the present status of the spin foam formulation of non-
perturbative (background-independent) quantum gravity. The topical review is divided into …

Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs
are dual to higher dimensional topological spaces. The perturbative development of the …

A large variety of interacting complex systems are characterized by interactions occurring
between more than two nodes. These systems are described by simplicial complexes …

Spin foam models are hoped to provide the dynamics of loop-quantum gravity. However, the
most popular of these, the Barrett-Crane model, does not have the good boundary state …

We provide a rather extended introduction to the group field theory approach to quantum
gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d …