Abstract:
At the microscopic scale, most crystals are composed of atoms which are arranged on a periodic lattice, which can be viewed as a minimizer of a certain interaction energy. The goal of this talk is to explain how to minimize some energies per particle among Bravais lattices of R^2, when the interaction potential is long-range. By using a result of Montgomery about theta functions, we will show several properties of optimality and non-optimality of the triangular lattice for these energies, with or without a density constraint. This talk is partially based on a joint work with Peng Zhang (Shanghai Jiao Tong University).