University of Minnesota Combinatorics Seminar: 2022

Date: 02/11/2022

Speaker: Terrence George

Dimers and Cross-Ratio Dynamics
Cross-ratio dynamics is a well known dynamical system in discrete differential geometry. It was recently shown to be integrable by Arnold, Fuchs, Izmestiev and Tabachnikov. We relate it to the cluster integrable system of Goncharov and Kenyon associated with the dimer model on a certain class of graphs. In particular, we find a cluster algebra structure describing cross-ratio dynamics. The talk is based on joint work (arXiv:2108.12692) with Niklas Affolter and Sanjay Ramassamy.

Dimers and Cross-Ratio Dynamics

Cross-ratio dynamics is a well known dynamical system in discrete differential geometry. It was recently shown to be integrable by Arnold, Fuchs, Izmestiev and Tabachnikov. We relate it to the cluster integrable system of Goncharov and Kenyon associated with the dimer model on a certain class of graphs. In particular, we find a cluster algebra structure describing cross-ratio dynamics. The talk is based on joint work (arXiv:2108.12692) with Niklas Affolter and Sanjay Ramassamy.