Cross-ratio dynamics is a discrete integrable system on the space of
polygons with vertices in CP^1. We relate an invariant Poisson structure
and integrals of motion recently found by
Arnold-Fuchs-Izmestiev-Tabachnikov for this system to the
Goncharov-Kenyon dimer integrable system considered on a specific class
of weighted graphs. We show that in some coordinates the dynamics is
described by geometric R-matrices, which solves the open question of
finding a cluster algebra structure describing cross-ratio dynamics. The
main tool relating geometry to the dimer model uses the notion of triple
crossing diagram maps, recently introduced by Affolter, Glick and myself.
This talk is based on joint work with Niklas Affolter (TU Berlin) and
Terrence George (University of Michigan).
The talk will be via Zoom at: