I review the current status of phenomenological programs inspired by quantum-spacetime
research. I stress in particular the significance of results establishing that certain data …

The status of multifractional theories is reviewed using comparative tables. Theoretical
foundations, classical matter and gravity dynamics, cosmology and experimental constraints …

We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety
program in quantum Einstein gravity. Using the continuum approach based upon the …

This paper is devoted to the development of local vector calculus in fractional-dimensional
spaces, on fractals, and in fractal continua. We conjecture that in the space of non-integer …

We review the present status of quantum-gravity phenomenology in relation to gravitational
waves (GWs). The topic can be approached from two directions, a model-dependent one …

We introduce fractional flat space, described by a continuous geometry with constant non-
integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but …

A bstract We construct a theory of fields living on continuous geometries with fractional
Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski …

A bstract The emergence of fractal features in the microscopic structure of space-time is a
common theme in many approaches to quantum gravity. In this work we carry out a detailed …

A review of different approaches to describe anisotropic fractal media is proposed. In this
paper, differentiation and integration non-integer dimensional and multi-fractional spaces …

Within the gravitational asymptotic safety program, the renormalization group (RG) flow of
the R 2 truncation in three and four spacetime dimensions is analyzed in detail. In particular …