He is professor at Université Paris 6, working at the laboratory for theoretical physics (LPT) of the École Normale Supérieure since 1986.

In using field theoretic techniques in the study of condensed matter, Brezin helped further modern theories of magnetism and the quantum Hall effect.

[5] He was awarded the 2011 Dirac Medal of the International Centre for Theoretical Physics together with John Cardy and Alexander Zamolodchikov.

He showed that the low temperature phase, in the case of a continuous symmetry break, is described by a non-linear sigma model, leading to a development of critical exponents in powers of the minus two space dimension.

He showed that the instantaneous method can be used to characterize the asymptotic behaviour of perturbation theory, thus allowing accurate theoretical estimates to be made.