In this article we describe the crystallization conjecture. It states that, in appropriate physical
conditions, interacting particles always place themselves into periodic configurations …

Our goal is to provide an introduction to the study of minimal energy problems, particularly
from the perspective of generating point configurations that provide useful discretizations of …

Algebraic combinatorics is the study of combinatorial objects as an extension of the study of
finite permutation groups, or, in other words, group theory without groups. In the spirit 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 …

Sylvia Serfaty is interested in developing analysis tools to understand problems from
physics. She has extensively studied the Ginzburg–Landau model of super-conductivity and …

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 …

The Cohn-Kumar conjecture states that the triangular lattice in dimension 2, the $ E_8 $
lattice in dimension 8, and the Leech lattice in dimension 24 are universally minimizing in …

In this paper, we study minimization problems among Bravais lattices for finite energy per
point. We first prove that if a function is completely monotonic, then the triangular lattice …

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 …