## ENSPM2021 Talk

**Title:** Emergent symmetries in critical 2D statistical physics

**Abstract:** A great achievement of physics in the second half of the twentieth century has been the prediction of conformal symmetry of the scaling limit of critical statistical physics systems. Around the turn of the millennium, the mathematical understanding of this fact progressed tremendously in two dimensions with the introduction of the Schramm-Loewner Evolution and the proofs of conformal invariance of the Ising model and dimers. Nevertheless, as for today the understanding remains restricted to very specific models. In this talk, we will introduce the notion of conformal invariance of lattice systems by taking the example of percolation models. We will also present some recent progress in the direction of proving full conformal invariance for a large class of such models. An important role will be played by a geometric interpretation of the notion of integrable system, and the notion of universality.

## Hugo Duminil-Copin (IHES, France, Geneve University, Switzerland)

French mathematician working on probability theory. He studied at the Lycée Louis-le-Grand in Paris, then the University Paris-Sud and the École normale supérieure (Paris). In 2008, he moved to the University of Geneva to write a PhD thesis under Stanislav Smirnov. In 2013, after his postdoctorate, he was appointed assistant professor, then professor, at the University of Geneva. In 2016, he became permanent professor at the Institut des Hautes Études Scientifiques and also win the Prize of the European Mathematical Society. In 2018 he was Invited speaker (session Probability and session Mathematical Physics) at the International Congress of Mathematicians of Rio de Janeiro.