I will review two combinatorial constructions of integrable systems: Goncharov-Kenyon construction based on counting perfect matchings in bipartite graphs, and Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on counting paths in networks. After that I will outline my proof of equivalence of those constructions.

The talk is based on this arXiv paper.

This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.