Geller received his undergraduate degree from the Conservatoire National des Arts et Métiers, Paris and his Doctorat en Sciences, under Prof. F. Perrin from the Sorbonne (1954).
He was hired in 1948 by F. Joliot Curie to work at Commissariat à l'énergie atomique (CEA; Atomic Energy Commission) and remained there until leaving in 1992, with the exception of a sabbatical at Stanford University (1961–1962), where, as a research associate, he developed the first bumpy torus plasma.
In the 1960s he developed electron cyclotron resonance heating of plasma physics as part of controlled fusion.
In 1992 he went to the Institut des Sciences Nucléaires de Grenoble, where he developed a new electron cyclotron resonance (ECR) method that was used to generate radioactive ion beams in nuclear physics.
[1] A prize awarded by Pantechnik (a manufacturer of ECR sources) is named after him and is delivered every 2 year at the ECRIS international conference.