This survey is mainly intended for non-specialists, though we try to include many recent
developments that may interest the experts as well. We want to study “good” finite subsets of …

This survey discusses recent developments in the context of spherical designs and minimal
energy point configurations on spheres. The recent solution of the long standing problem of …

The problem of retrieving phase information from amplitude measurements alone has
appeared in many scientific disciplines over the last century. PhaseLift is a recently …

A complex projective $ t $-design is a configuration of vectors which is``evenly distributed''on
a sphere in the sense that sampling uniformly from it reproduces the moments of Haar …

We study the Hamiltonian of a two-dimensional log-gas with a confining potential V
satisfying the weak growth assumption—V is of the same order as 2\log ‖ x ‖ 2 log‖ x …

We define some new polynomials associated to a linear binary code and a harmonic
function of degree k. The case k= 0 is the usual weight enumerator of the code. When …

We introduce the notion of at-design on the Grassmann manifold G _ m, n of the m-
subspaces of the Euclidean space R n. It generalizes the notion of antipodal spherical …

Cubature formulas and geometrical designs are described in terms of reproducing kernels
for Hilbert spaces of functions on the one hand, and Markov operators associated to …

We consider the minimization of theta functions 𝜃 Λ (α)=∑ p∈ Λ e− π α| p| 2 amongst
periodic configurations Λ⊂ R d⁠, by reducing the dimension of the problem, following as a …

We investigate the local and global optimality of the triangular, square, simple cubic, face-
centered-cubic (fcc) and body-centered-cubic (bcc) lattices and the hexagonal-close …