Gregory Hugh Wannier (born 30.12.1911) is a theoretical physicist. He was born in Basel. In 1935 he received the degree of doctor of mathematical physics at the University of Basel. In 1935 — 36 he worked at the University of Geneva, in 1936 —37 at Princeton, in 1938-39 at Bristol, in 1939 — 41 at Texas, in 1941—46 at the University of Iowa and in 1949 — 60 at Bell Laboratories. From 1960 he was professor at the University of Oregon.
His research concerned the theory of solids, magnetism, statistical mechanics, discharges in gases and electron physics. He studied molecular and crystal structures, the localisation of electrons in a solid, and phase transitions. In 1937, independently of N. Mott, he developed the idea of a bound state of an electron from the conduction band and a hole from the valence band (the Wannier–Mott exciton). He laid the foundations of the theory of excitons. In the theory of magnetism he introduced (1937) orthogonal functions (Wannier functions) and proposed a method of investigating the band structure of solids based on these functions.