Abel Klein (born January 16, 1945) is a Brazilian-American mathematician, specializing in mathematical physics and, more specifically, random Schrödinger operators for disordered systems.
[1] He received in 1971 his PhD from the Massachusetts Institute of Technology under the supervision of Irving Segal with the thesis Regularity and Covariance Properties of Quantum Fields with Applications to Currents and Generalized Free Fields.
In the widely accepted picture, in three or more dimensions there exists a transition from an insulator region, characterized by localized states, to a very different metallic region, characterized by extended states, while in one or two dimensions there are only localized states and no metal-insulator transition.
Klein's research aims to further the mathematical understanding of this picture.
[3] In 2012 he was elected a Fellow of the American Mathematical Society.