Dimers and Integrability

Dimers and Integrability - Richard Kenyon

Richard Kenyon
Brown University
March 29, 2013

This is joint work with A. B. Goncharov. To any convex integer polygon we associate a Poisson variety, which is essentially the moduli space of connections on line bundles on (certain) bipartite graphs on a torus. There is an underlying integrable Hamiltonian system whose Hamiltonians are weighted sums of dimer covers.