Dimers, clusters, integrability

Dimer model on a bipartite graph on a torus
gives rise to an integrable system of a special kind - cluster
integrable system.
Its Hamiltonians are components of the
partition function of the dimer model.
In certain cases we get discrete integrable systems,
which contain discretizations of KP and BKP equations.

This is a joint work with R. Kenyon.