Hamiltonian Systems

Event Information Cross-ratio dynamics and the dimer cluster integrable system
12:00 on Tuesday February 08, 2022
13:30 on Tuesday February 08, 2022
Sanjay Ramassamy

CNRS, Institut de Physique Théorique (CEA Saclay)

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: https://utoronto.zoom.us/j/99576627828

Passcode: 448487