ИСТИНА

he talk is focused on three related topics: electrical networks, polynomial graph invariants and the Ising-type models. All of them possess the same characteristic properties to be an integrable statistical model, to be a cluster variety and to be inherent to some nontrivial combinatorial problem. I will explain the similarity between these tasks and present the substantial algebraic structure behind. The talk is based on some recent works with V. Gorbounov https://arxiv.org/abs/1905.03522 and B. Bychkov and A. Kazakov https://arxiv.org/abs/2005.10288.