After two decades of development, cavity quantum electrodynamics with superconducting
circuits has emerged as a rich platform for quantum computation and simulation. Lattices of …

Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum
simulation and computation. In recent groundbreaking experiments, the immense flexibility …

The idea of self-similarity is one of the most fundamental in the modern mathematics. The
notion of “renormalization group”, which plays an essential role in quantum field theory …

We adapt to a family of hyperbolic buildings of dimension two, some geometric quasi-
conformal arguments which are classical in the case of rank one non compact symmetric …

We review some known results and open problems related to the growth of groups. For a
finitely generated group Γ, given whenever necessary together with a finite generating set …

We investigate the dynamic properties of elastic lattices defined by tessellations of a curved
hyperbolic space. The lattices are obtained by our projecting nodes of a regular hyperbolic …

The shortest loop traced out by a billiard ball in an acute triangle is the pedal subtriangle,
connecting the feet of the altitudes. In this paper we prove a similar result for loops in the …

Foliations, groups and pseudogroups are objects which are closely related via the notion of
holonomy. In the 1980s they became considered as general dynamical systems. This book …

The random-cluster model is a dependent percolation model that has applications in the
study of Ising and Potts models. In this paper, several new results are obtained for the …

The Euler characteristic of a cell complex is often thought of as the alternating sum of the
number of cells of each dimension. When the complex is infinite, the sum diverges …