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.