Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field
theories, in particular for quantum gravity. Significant progress on this program has led to a …

Asymptotic safety describes a scenario in which general relativity can be quantized as a
conventional field theory, despite being nonrenormalizable when expanding it around a …

We introduce a new basis on the state space of nonperturbative quantum gravity. The states
of this basis are linearly independent, are well defined in both the loop representation and …

This graduate level text describes in a unified fashion the statistical mechanics of random
walks, random surfaces and random higher dimensional manifolds with an emphasis on the …

Quantum gravity is the missing piece in our understanding of the fundamental interactions
today. Given recent observational breakthroughs in gravity, providing a quantum theory for …

A model is proposed which generates all oriented 3D simplicial complexes weighted with an
invariant associated with a topological lattice gauge theory. When the gauge group is SUq …

The construction of a consistent theory of quantum gravity is a problem in theoretical physics
that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial …

The aim of this chapter is to explain carefully the arguments behind the assertion that the
correct quantum theory of gravity must be background independent. We begin by recounting …

We present a simple algebraic mechanism for the emergence of deformations of Poincaré
symmetries in the low-energy limit of quantum theories of gravity. The deformations, called κ …

A one parameter family of retarded linear operators on scalar fields on causal sets is
introduced. When the causal set is well approximated by 4 dimensional Minkowski …