Thomas Leblé: Local optimality of the hexagonal lattice

par Thomas Leblé

vendredi 30 janv. 2026, 09:30 → 12:00 Europe/Paris

Fokko Du cloux (UCBL Bâtiment Braconnier)

If one tries to arrange 1 euro coins on a table in the most compact way, one should place the centers of the coins on the sites of an hexagonal lattice. This is the planar version of the famous Kepler conjecture stating that BCC and FCC lattices are the most compact sphere packings - and it is significantly easier.

In dimension 2, it is believed that the hexagonal lattice also gives the optimal configuration of points for a whole family of energy minimization problems (e.g. distributing electrons in a classical jellium or vortices in a superfluid). This is sometimes referred to as the "Abrikosov conjecture", and in the mathematics literature, this has been known recently as the Cohn-Kumar "universal optimality" conjecture.

I will present what is known about this question - not so much, in fact much more is known in dimension 8 and 24 thanks to the works of Viazovska et al. - including a recent local optimality result.