University of Minnesota Combinatorics Seminar: 2021-2022

Date: 10/08/2021

Speaker: Anton Izosimov

Dimers, Networks, and Integrable Systems
There are two well known constructions that build an integrable system out of a graph on a torus (with some additional structure). One is the Goncharov-Kenyon construction which assumes that the graph is bipartite and employs the dimer partition function. The other one, due to Gekhtman, Shapiro, Tabachnikov, and Vainshtein, applies to perfect networks and utilizes the boundary measurement matrix. In the talk I will explain my recent proof of equivalence of those constructions. No knowledge of integrable systems is required to understand the talk.

Dimers, Networks, and Integrable Systems

There are two well known constructions that build an integrable system out of a graph on a torus (with some additional structure). One is the Goncharov-Kenyon construction which assumes that the graph is bipartite and employs the dimer partition function. The other one, due to Gekhtman, Shapiro, Tabachnikov, and Vainshtein, applies to perfect networks and utilizes the boundary measurement matrix. In the talk I will explain my recent proof of equivalence of those constructions. No knowledge of integrable systems is required to understand the talk.