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.
This is joint work with A. B. Goncharov.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
