The Conformal Bootstrap Approach to Criticality in 3 and 2+1 Dimensions

The standard view of critical phenomena, such as the liquid-gas critical point or the Curie temperature of a ferromagnet, is through the Renormalization Group. I will describe an alternative – view it as a self-consistent “soup” of interacting fluctuations, governed by tight equations of Conformal Field Theory. This approach is both rigorous and calculable, with unprecedented precision for the 3D Ising model critical exponents.