Abstract: This is joint work with Robin Pemantle. Two recurrence relations which are fundamental in combinatorics, integrable systems, and statistical mechanics are the "octahedron recurrence" also known as Hirota's bilinear difference equation, and "cube recurrence" or Miwa equation. We introduce a cousin of these, dubbed the "hexahedron recurrence", show how it is related to the Ising model, and in particular show how this uncovers a cluster algebra structure in the Ising model.

This talk will be accessible to graduate students.