  These notes provide an introduction to recent work by Kevin Costello in which
integrable lattice models of classical statistical mechanics in two dimensions
are understood in terms of quantum gauge theory in four dimensions. This
construction will be compared to the more familiar relationship between quantum
knot invariants in three dimensions and Chern-Simons gauge theory. (Based on a
Whittaker Colloquium at the University of Edinburgh and a lecture at Strings
2016 in Beijing.)
