Short Talk: Paul Cahen

The Ising model is one of the most known model of statistical mechanics. It exhibits a phase transition and, in the planar case it possesses at its critical point a very strong property: it is conformal invariant (and it is one of the very few models for which this has been derived rigorously). These reasons justify (among many others) the interest mathematicians put and are putting into it. However, even in dimension two, there are still things that remain mysterious. One of the aim of my joint work with Garban and Sepúlveda is to investigate the relationships between two different viewpoints that were used to analyze conformal invariance: interfaces between clusters of spins and the magnetization field.