Ruth and Irving Adler Expository Lecture in Mathematics

The physicist Abrikosov predicted that in certain superconductors, one should observe triangular lattices of vortices, now called Abrikosov lattices.  When studying ground states of Coulomb gases, which is motivated by questions in approximation theory, random matrix theory and statistical physics, one also expects the same lattices to appear.  This crystallization phenomenon turns out to be related to the Cohn-Kumar conjecture about the universal minimality of certain special lattices in dimensions 2, 8 and 24 and recently solved in dimensions 8 and 24.