  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 the sense that they minimize the total pair
interaction energy of infinite point configurations for all completely monotone
functions of the squared distance. This conjecture was recently proved by
Cohn-Kumar-Miller-Radchenko-Viazovska in dimensions 8 and 24. We explain in
this note how the conjecture implies the minimality of the same lattices for
the Coulomb and Riesz renormalized energies as well as jellium and periodic
jellium energies, hence settling the question of their minimization in
dimensions 8 and 24.
