Hugo Duminil-Copin

fl. 1985, Châtenay-Malabry, France

Probability and statisticsMathematical physicsFields Medal 2022

French probabilist at IHÉS and the University of Geneva, known for rigorous results on phase transitions in lattice models; Fields Medalist 2022.

Hugo Duminil-Copin was born in Châtenay-Malabry near Paris and grew up partly in Martinique. He studied at the École normale supérieure in Paris and completed his PhD at the University of Geneva in 2012 under Stanislav Smirnov, working on two-dimensional lattice models of statistical mechanics.

After a postdoc, he became professor at the University of Geneva and, in 2016, permanent professor at the Institut des Hautes Études Scientifiques (IHÉS) in Bures-sur-Yvette, holding both positions. His research transforms the probabilistic study of phase transitions: Ising and Potts models, Fortuin–Kasteleyn percolation, and self-avoiding walks.

Among his signature results are the joint proof with Smirnov that the connective constant of the hexagonal lattice equals $\sqrt{2+\sqrt{2}}$ (2012), the sharpness of the phase transition in a wide class of percolation models, and with Aizenman the triviality of the four-dimensional $\varphi^4$ theory. He received the Fields Medal in 2022.

Workplaces: Institut des Hautes Études Scientifiques (IHÉS), University of Geneva

France

Award-winning work

Fields Medal 2022Duminil-Copin was awarded the medal for solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four. With collaborators he established the continuity and sharpness of the phase transition of the Ising model in dimension three — questions open since the 1980s — and, with Aizenman, proved mean-field critical behaviour of the four-dimensional Ising model and the triviality of four-dimensional Euclidean scalar quantum field theory, a physics conjecture dating to the 1970s. For two-dimensional Fortuin–Kasteleyn percolation he determined continuity or discontinuity of the transition for all parameter values and proved rotational invariance at large scales, a key step toward conformal invariance. He also settled, with Smirnov, the connective constant of self-avoiding walks on the hexagonal lattice.

Contributions, linked to the library

Great problemCritical exponents of self-avoiding walksWith Smirnov, determined the connective constant of self-avoiding walks on the hexagonal lattice,

\sqrt{2+\sqrt{2}}

.Great problemContinuity of the phase transition in 3D percolationHis sharpness and continuity results for Ising and FK percolation settle, in low dimensions, questions closely related to the continuity of percolation transitions.Library topicStochastic processes and Markov chainsDeveloped probabilistic tools — sharp thresholds, randomized-cluster representations — that turned lattice phase transitions into rigorous random processes.