Mathematics Colloquium

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Emerging symmetries in 2D percolation

Speaker: Hugo Duminil-Copin, Université de Genève and IHES.

Location: Online

Date: Monday, March 8, 2021, 3:45 p.m.

Synopsis:

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, the understanding is still restricted to very specific models. In this talk, we will gently introduce the notion of conformal invariance of lattice systems by taking the example of percolation models. We will also explain some recent proof of rotational invariance for a large class of such models. This represents an important progress in the direction of proving full conformal invariance.