Abstract: Integrable models of statistical mechanics in two dimensions, such as the Ising model, have provided important and surprising examples and have been studied from many points of view by both physicists and mathematicians. In recent years, Kevin Costello has developed a new approach to these models, using a four-dimensional cousin of three-dimensional Chern-Simons gauge theory in which the spectral parameter'' has a geometric explanation. This talk will be primarily an introduction to the work of Costello.