ИСТИНА

The exposition will be devoted to the latest advances in the theory of electric varieties, based on the joint work with V. Gorbunov https://arxiv.org/abs/1905.03522. This classical subject demonstrates the properties typical for cluster varieties and broadly inherits the structures of integrable statistical mechanics. I will talk about the Lusztig problem, its deformation providing a boundary measurement matrix for an electrical network, a representation of the Temperley-Lieb TL(0) algebra and integrable discrete dynamics on some electrical varieties.