Hugo Duminil-Copin (Université de Genève)

Physical systems may abruptly change their macroscopic behavior as one of their thermodynamical quantities varies through a critical point. In this talk, we describe two ways of computing critical points for statistical physics models through two important examples (the so-called FK percolation and the Self-Avoiding Walk model). Identifying these points is a crucial step towards the understanding of the phase transition for these models. We will insist on standard techniques used in rigorous planar statistical physics (such as coupling and duality arguments) and on two novel techniques (sharp threshold and discrete holomorphicity) developed over the past few years. The talk is partly based on joint works with V. Beffara and S. Smirnov. It will be accessible to a general mathematical audience.