Probability Seminar | Field Theory of the Planar Ising Model

The conjecture that the critical Ising model is conformally invariant has been given rigorous justifications from the viewpoints of both Conformal Field Theory (CFT) and Schramm-Loewner Evolutions (SLE), thanks in large part to the discrete complex analytic viewpoint pioneered by Smirnov and others. We give an overview of major results and mathematical ideas, as well as some historical and physical contexts. We will end by presenting recent progress on moving beyond the conformally invariant descriptions. Based on joint works with Chelkak, Izyurov, Webb, and others.